Lambda-CDM model

The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

a cosmological constant, denoted by lambda (Λ), associated with dark energy
the postulated cold dark matter, denoted by CDM
ordinary matter

It is referred to as the standard model of Big Bang cosmology^[1] because it is the simplest model that provides a reasonably good account of:

the existence and structure of the cosmic microwave background
the large-scale structure in the distribution of galaxies
the observed abundances of hydrogen (including deuterium), helium, and lithium
the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, entropic gravity, modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity, scale invariance of empty space, and decaying dark matter (DDM).^[2]^[3]^[4]^[5]^[6]

Remove ads

The ΛCDM model includes an expansion of metric space that is well documented, both as the redshift of prominent spectral absorption or emission lines in the light from distant galaxies, and as the time dilation in the light decay of supernova luminosity curves. Both effects are attributed to a Doppler shift in electromagnetic radiation as it travels across expanding space. Although this expansion increases the distance between objects that are not under shared gravitational influence, it does not increase the size of the objects (e.g. galaxies) in space. Also, since it originates from ordinary general relativity, it, like general relativity, allows for distant galaxies to recede from each other at speeds greater than the speed of light; local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light.^[7]

The letter Λ (lambda) represents the cosmological constant, which is associated with a vacuum energy or dark energy in empty space that is used to explain the contemporary accelerating expansion of space against the attractive effects of gravity. A cosmological constant has negative pressure, $p=-\rho c^{2}$ , which contributes to the stress–energy tensor that, according to the general theory of relativity, causes accelerating expansion. The fraction of the total energy density of our (flat or almost flat) universe that is dark energy, $\Omega _{\Lambda }$ , is estimated to be 0.669 ± 0.038 based on the 2018 Dark Energy Survey results using Type Ia supernovae^[8] or 0.6847±0.0073 based on the 2018 release of Planck satellite data, or more than 68.3 % (2018 estimate) of the mass–energy density of the universe.^[9]

Dark matter is postulated in order to account for gravitational effects observed in very large-scale structures (the "non-keplerian" rotation curves of galaxies;^[10] the gravitational lensing of light by galaxy clusters; and the enhanced clustering of galaxies) that cannot be accounted for by the quantity of observed matter.^[11] The ΛCDM model proposes specifically cold dark matter, hypothesized as:

Non-baryonic: Consists of matter other than protons and neutrons (and electrons, by convention, although electrons are not baryons)
Cold: Its velocity is far less than the speed of light at the epoch of radiation–matter equality (thus neutrinos are excluded, being non-baryonic but not cold)
Dissipationless: Cannot cool by radiating photons
Collisionless: Dark matter particles interact with each other and other particles only through gravity and possibly the weak force

Dark matter constitutes about 26.5 %^[12] of the mass–energy density of the universe. The remaining 4.9 %^[12] comprises all ordinary matter observed as atoms, chemical elements, gas and plasma, the stuff of which visible planets, stars and galaxies are made. The great majority of ordinary matter in the universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10 % of the ordinary matter contribution to the mass–energy density of the universe.^[13]

The model includes a single originating event, the "Big Bang", which was not an explosion but the abrupt appearance of expanding spacetime containing radiation at temperatures of around 10¹⁵ K. This was immediately (within 10⁻²⁹ seconds) followed by an exponential expansion of space by a scale multiplier of 10²⁷ or more, known as cosmic inflation. The early universe remained hot (above 10 000 K) for several hundred thousand years, a state that is detectable as a residual cosmic microwave background, or CMB, a very low-energy radiation emanating from all parts of the sky. The "Big Bang" scenario, with cosmic inflation and standard particle physics, is the only cosmological model consistent with the observed continuing expansion of space, the observed distribution of lighter elements in the universe (hydrogen, helium, and lithium), and the spatial texture of minute irregularities (anisotropies) in the CMB radiation. Cosmic inflation also addresses the "horizon problem" in the CMB; indeed, it seems likely that the universe is larger than the observable particle horizon.^{[citation needed]}

The model uses the Friedmann–Lemaître–Robertson–Walker metric, the Friedmann equations, and the cosmological equations of state to describe the observable universe from approximately 0.1 s to the present.^[1]^: 605

Remove ads

The expansion of the universe is parameterized by a dimensionless scale factor $a=a(t)$ (with time $t$ counted from the birth of the universe), defined relative to the present time, so $a_{0}=a(t_{0})=1$ ; the usual convention in cosmology is that subscript 0 denotes present-day values, so $t_{0}$ denotes the age of the universe. The scale factor is related to the observed redshift^[14] $z$ of the light emitted at time $t_{\mathrm {em} }$ by

a(t_{\text{em}})={\frac {1}{1+z}}\,.

The expansion rate is described by the time-dependent Hubble parameter, $H(t)$ , defined as

H(t)\equiv {\frac {\dot {a}}{a}},

where ${\dot {a}}$ is the time-derivative of the scale factor. The first Friedmann equation gives the expansion rate in terms of the matter+radiation density $\rho$ , the curvature $k$ , and the cosmological constant $\Lambda$ ,^[14]

H^{2}=\left({\frac {\dot {a}}{a}}\right)^{2}={\frac {8\pi G}{3}}\rho -{\frac {kc^{2}}{a^{2}}}+{\frac {\Lambda c^{2}}{3}},

where, as usual $c$ is the speed of light and $G$ is the gravitational constant. A critical density $\rho _{\mathrm {crit} }$ is the present-day density, which gives zero curvature $k$ , assuming the cosmological constant $\Lambda$ is zero, regardless of its actual value. Substituting these conditions to the Friedmann equation gives

\rho _{\mathrm {crit} }={\frac {3H_{0}^{2}}{8\pi G}}=1.878\;47(23)\times 10^{-26}\;h^{2}\;\mathrm {kg{\cdot }m^{-3}} ,

^[15]

where $h\equiv H_{0}/(100\;\mathrm {km{\cdot }s^{-1}{\cdot }Mpc^{-1}} )$ is the reduced Hubble constant. If the cosmological constant were actually zero, the critical density would also mark the dividing line between eventual recollapse of the universe to a Big Crunch, or unlimited expansion. For the Lambda-CDM model with a positive cosmological constant (as observed), the universe is predicted to expand forever regardless of whether the total density is slightly above or below the critical density; though other outcomes are possible in extended models where the dark energy is not constant but actually time-dependent.^{[citation needed]}

It is standard to define the present-day density parameter $\Omega _{x}$ for various species as the dimensionless ratio

\Omega _{x}\equiv {\frac {\rho _{x}(t=t_{0})}{\rho _{\mathrm {crit} }}}={\frac {8\pi G\rho _{x}(t=t_{0})}{3H_{0}^{2}}}

where the subscript $x$ is one of $\mathrm {b}$ for baryons, $\mathrm {c}$ for cold dark matter, $\mathrm {rad}$ for radiation (photons plus relativistic neutrinos), and $\Lambda$ for dark energy.^{[citation needed]}

Since the densities of various species scale as different powers of $a$ , e.g. $a^{-3}$ for matter etc., the Friedmann equation can be conveniently rewritten in terms of the various density parameters as

H(a)\equiv {\frac {\dot {a}}{a}}=H_{0}{\sqrt {(\Omega _{\rm {c}}+\Omega _{\rm {b}})a^{-3}+\Omega _{\mathrm {rad} }a^{-4}+\Omega _{k}a^{-2}+\Omega _{\Lambda }a^{-3(1+w)}}},

where $w$ is the equation of state parameter of dark energy, and assuming negligible neutrino mass (significant neutrino mass requires a more complex equation). The various $\Omega$ parameters add up to $1$ by construction. In the general case this is integrated by computer to give the expansion history $a(t)$ and also observable distance–redshift relations for any chosen values of the cosmological parameters, which can then be compared with observations such as supernovae and baryon acoustic oscillations.^{[citation needed]}

In the minimal 6-parameter Lambda-CDM model, it is assumed that curvature $\Omega _{k}$ is zero and $w=-1$ , so this simplifies to

H(a)=H_{0}{\sqrt {\Omega _{\rm {m}}a^{-3}+\Omega _{\mathrm {rad} }a^{-4}+\Omega _{\Lambda }}}

Observations show that the radiation density is very small today, $\Omega _{\text{rad}}\sim 10^{-4}$ ; if this term is neglected the above has an analytic solution^[16]

a(t)=(\Omega _{\rm {m}}/\Omega _{\Lambda })^{1/3}\,\sinh ^{2/3}(t/t_{\Lambda })

where ${\displaystyle t_{\Lambda }\equiv 2/(3H_{0}{\sqrt {\Omega _{\Lambda }}})\$ this is fairly accurate for $a>0.01$ or $t>10$ million years. Solving for $a(t)=1$ gives the present age of the universe $t_{0}$ in terms of the other parameters.^{[citation needed]}

It follows that the transition from decelerating to accelerating expansion (the second derivative ${\ddot {a}}$ crossing zero) occurred when

a=(\Omega _{\rm {m}}/2\Omega _{\Lambda })^{1/3},

which evaluates to $a\sim 0.6$ or $z\sim 0.66$ for the best-fit parameters estimated from the Planck spacecraft.^{[citation needed]}

Remove ads

The discovery of the cosmic microwave background (CMB) in 1964 confirmed a key prediction of the Big Bang cosmology. From that point on, it was generally accepted that the universe started in a hot, dense state and has been expanding over time. The rate of expansion depends on the types of matter and energy present in the universe, and in particular, whether the total density is above or below the so-called critical density.^{[citation needed]}

During the 1970s, most attention focused on pure-baryonic models, but there were serious challenges explaining the formation of galaxies, given the small anisotropies in the CMB (upper limits at that time). In the early 1980s, it was realized that this could be resolved if cold dark matter dominated over the baryons, and the theory of cosmic inflation motivated models with critical density.^{[citation needed]}

During the 1980s, most research focused on cold dark matter with critical density in matter, around 95 % CDM and 5 % baryons: these showed success at forming galaxies and clusters of galaxies, but problems remained; notably, the model required a Hubble constant lower than preferred by observations, and observations around 1988–1990 showed more large-scale galaxy clustering than predicted.^{[citation needed]}

These difficulties sharpened with the discovery of CMB anisotropy by the Cosmic Background Explorer in 1992, and several modified CDM models, including ΛCDM and mixed cold and hot dark matter, came under active consideration through the mid-1990s. The ΛCDM model then became the leading model following the observations of accelerating expansion in 1998, and was quickly supported by other observations: in 2000, the BOOMERanG microwave background experiment measured the total (matter–energy) density to be close to 100 % of critical, whereas in 2001 the 2dFGRS galaxy redshift survey measured the matter density to be near 25 %; the large difference between these values supports a positive Λ or dark energy. Much more precise spacecraft measurements of the microwave background from WMAP in 2003–2010 and Planck in 2013–2015 have continued to support the model and pin down the parameter values, most of which are constrained below 1 percent uncertainty.^{[citation needed]}

Research is active into many aspects of the ΛCDM model, both to refine the parameters and to resolve the tensions between recent observations and the ΛCDM model, such as the Hubble tension and the CMB dipole.^[17] In addition, ΛCDM has no explicit physical theory for the origin or physical nature of dark matter or dark energy; the nearly scale-invariant spectrum of the CMB perturbations, and their image across the celestial sphere, are believed to result from very small thermal and acoustic irregularities at the point of recombination.^{[citation needed]}

Historically, a large majority of astronomers and astrophysicists support the ΛCDM model or close relatives of it, but recent observations that contradict the ΛCDM model have led some astronomers and astrophysicists to search for alternatives to the ΛCDM model, which include dropping the Friedmann–Lemaître–Robertson–Walker metric or modifying dark energy.^[17]^[18] On the other hand, Milgrom, McGaugh, and Kroupa have long been leading critics of the ΛCDM model, attacking the dark matter portions of the theory from the perspective of galaxy formation models and supporting the alternative modified Newtonian dynamics (MOND) theory, which requires a modification of the Einstein field equations and the Friedmann equations as seen in proposals such as modified gravity theory (MOG theory) or tensor–vector–scalar gravity theory (TeVeS theory). Other proposals by theoretical astrophysicists of cosmological alternatives to Einstein's general relativity that attempt to account for dark energy or dark matter include f(R) gravity, scalar–tensor theories such as galileon [ko] theories (see Galilean invariance), brane cosmologies, the DGP model, and massive gravity and its extensions such as bimetric gravity.^{[citation needed]}

Remove ads

In addition to explaining many pre-2000 observations, the model has made a number of successful predictions: notably the existence of the baryon acoustic oscillation feature, discovered in 2005 in the predicted location; and the statistics of weak gravitational lensing, first observed in 2000 by several teams. The polarization of the CMB, discovered in 2002 by DASI,^[19] has been successfully predicted by the model: in the 2015 Planck data release,^[20] there are seven observed peaks in the temperature (TT) power spectrum, six peaks in the temperature–polarization (TE) cross spectrum, and five peaks in the polarization (EE) spectrum. The six free parameters can be well constrained by the TT spectrum alone, and then the TE and EE spectra can be predicted theoretically to few-percent precision with no further adjustments allowed.^{[citation needed]}

Remove ads

Over the years, numerous simulations of ΛCDM and observations of our universe have been made that challenge the validity of the ΛCDM model, to the point where some cosmologists believe that the ΛCDM model may be superseded by a different, as yet unknown cosmological model.^[17]^[18]^[21]

Lack of detection

Extensive searches for dark matter particles have so far shown no well-agreed detection, while dark energy may be almost impossible to detect in a laboratory, and its value is extremely small compared to vacuum energy theoretical predictions.^{[citation needed]}

Violations of the cosmological principle

The ΛCDM model has been shown to satisfy the cosmological principle, which states that, on a large-enough scale, the universe looks the same in all directions (isotropy) and from every location (homogeneity); "the universe looks the same whoever and wherever you are."^[22] The cosmological principle exists because when the predecessors of the ΛCDM model were being developed, there was not sufficient data available to distinguish between more complex anisotropic or inhomogeneous models, so homogeneity and isotropy were assumed to simplify the models,^[23] and the assumptions were carried over into the ΛCDM model.^[24] However, recent findings have suggested that violations of the cosmological principle, especially of isotropy, exist. These violations have called the ΛCDM model into question, with some authors suggesting that the cosmological principle is obsolete or that the Friedmann–Lemaître–Robertson–Walker metric breaks down in the late universe.^[17]^[25]^[26] This has additional implications for the validity of the cosmological constant in the ΛCDM model, as dark energy is implied by observations only if the cosmological principle is true.^[27]^[24]

Violations of isotropy

Evidence from galaxy clusters,^[28]^[29] quasars,^[30] and type Ia supernovae^[31] suggest that isotropy is violated on large scales.^{[citation needed]}

Data from the Planck Mission shows hemispheric bias in the cosmic microwave background in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies in the CMB are, in fact, statistically significant and can no longer be ignored.^[32]

Already in 1967, Dennis Sciama predicted that the cosmic microwave background has a significant dipole anisotropy.^[33]^[34] In recent years, the CMB dipole has been tested, and the results suggest our motion with respect to distant radio galaxies^[35] and quasars^[36] differs from our motion with respect to the cosmic microwave background. The same conclusion has been reached in recent studies of the Hubble diagram of Type Ia supernovae^[37] and quasars.^[38] This contradicts the cosmological principle.^{[citation needed]}

The CMB dipole is hinted at through a number of other observations. First, even within the cosmic microwave background, there are curious directional alignments^[39] and an anomalous parity asymmetry^[40] that may have an origin in the CMB dipole.^[41] Separately, the CMB dipole direction has emerged as a preferred direction in studies of alignments in quasar polarizations,^[42] scaling relations in galaxy clusters,^[43]^[44] strong lensing time delay,^[25] Type Ia supernovae,^[45] and quasars and gamma-ray bursts as standard candles.^[46] The fact that all these independent observables, based on different physics, are tracking the CMB dipole direction suggests that the Universe is anisotropic in the direction of the CMB dipole.^{[citation needed]}

Nevertheless, some authors have stated that the universe around Earth is isotropic at high significance by studies of the cosmic microwave background temperature maps.^[47]

Violations of homogeneity

Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.^[48] However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including

The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc
The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc^[49]
U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc
The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)^[50]
The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc^[51]
The Big Ring, reported in 2024, which has a diameter of 399 Mpc and is shaped like a ring^[52]

Other authors claim that the existence of structures larger than the scale of homogeneity in the ΛCDM model does not necessarily violate the cosmological principle in the ΛCDM model.^[53]^[17]

El Gordo galaxy cluster collision

El Gordo is a massive interacting galaxy cluster in the early Universe ( $z=0.87$ ). The extreme properties of El Gordo in terms of its redshift, mass, and the collision velocity leads to strong ( $6.16\sigma$ ) tension with the ΛCDM model.^[54]^[55] The properties of El Gordo are however consistent with cosmological simulations in the framework of MOND due to more rapid structure formation.^[56]

KBC void

The KBC void is an immense, comparatively empty region of space containing the Milky Way approximately 2 billion light-years (600 megaparsecs, Mpc) in diameter.^[57]^[58]^[17] Some authors have said the existence of the KBC void violates the assumption that the CMB reflects baryonic density fluctuations at $z=1100$ or Einstein's theory of general relativity, either of which would violate the ΛCDM model,^[59] while other authors have claimed that supervoids as large as the KBC void are consistent with the ΛCDM model.^[60]

Hubble tension

Statistically significant differences remain in measurements of the Hubble constant based on the cosmic background radiation compared to astronomical distance measurements. This difference has been called the Hubble tension.^[61]

The Hubble tension in cosmology is widely acknowledged to be a major problem for the ΛCDM model.^[18]^[62]^[17]^[21] In December 2021, National Geographic reported that the cause of the Hubble tension discrepancy is not known.^[63] However, if the cosmological principle fails (see Violations of the cosmological principle), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension.^[17]^[25]

Some authors postulate that the Hubble tension can be explained entirely by the KBC void, as measuring galactic supernovae inside a void is predicted by the authors to yield a larger local value for the Hubble constant than cosmological measures of the Hubble constant.^[64] However, other work has found no evidence for this in observations, finding the scale of the claimed underdensity to be incompatible with observations which extend beyond its radius.^[65] Important deficiencies were subsequently pointed out in this analysis, leaving open the possibility that the Hubble tension is indeed caused by outflow from the KBC void.^[59]

As a result of the Hubble tension, other researchers have called for new physics beyond the ΛCDM model.^[61] Moritz Haslbauer et al. proposed that MOND would resolve the Hubble tension.^[59] Another group of researchers led by Marc Kamionkowski proposed a cosmological model with early dark energy to replace ΛCDM.^[66]

S₈ tension

The $S_{8}$ tension in cosmology is another major problem for the ΛCDM model.^[17] The $S_{8}$ parameter in the ΛCDM model quantifies the amplitude of matter fluctuations in the late universe and is defined as

S_{8}\equiv \sigma _{8}{\sqrt {\Omega _{\rm {m}}/0.3}}

Early- (e.g. from CMB data collected using the Planck observatory) and late-time (e.g. measuring weak gravitational lensing events) facilitate increasingly precise values of $S_{8}$ . However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy is called the $S_{8}$ tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that the ΛCDM model may be incomplete or in need of correction.^[17]

Some values for $S_{8}$ are 0.832±0.013 (2020 Planck),^[67] 0.766+0.020
−0.014 (2021 KIDS),^[68]^[69] 0.776±0.017 (2022 DES),^[70] 0.790+0.018
−0.014 (2023 DES+KIDS),^[71] 0.769+0.031
−0.034 – 0.776+0.032
−0.033^[72]^[73]^[74]^[75] (2023 HSC-SSP), 0.86±0.01 (2024 EROSITA).^[76]^[77] Values have also obtained using peculiar velocities, 0.637±0.054 (2020)^[78] and 0.776±0.033 (2020),^[79] among other methods.

Axis of evil

The "axis of evil" is a name given to an unsubstantiated correlation between the plane of the Solar System and aspects of the cosmic microwave background (CMB). It gives the plane of the Solar System and hence the location of Earth a greater significance than might be expected by chance – a result which has been claimed to be evidence of a departure from the Copernican principle.^[80] Later analysis found no such evidence.^[81]

Cosmological lithium problem

The actual observable amount of lithium in the universe is less than the calculated amount from the ΛCDM model by a factor of 3–4.^[82]^[17] If every calculation is correct, then solutions beyond the existing ΛCDM model might be needed.^[82]

Shape of the universe

The ΛCDM model assumes that the shape of the universe is of zero curvature (is flat) and has an undetermined topology. In 2019, interpretation of Planck data suggested that the curvature of the universe might be positive (often called "closed"), which would contradict the ΛCDM model.^[83]^[17] Some authors have suggested that the Planck data detecting a positive curvature could be evidence of a local inhomogeneity in the curvature of the universe rather than the universe actually being globally a 3-manifold of positive curvature.^[84]^[17]

Violations of the strong equivalence principle

The ΛCDM model assumes that the strong equivalence principle is true. However, in 2020 a group of astronomers analyzed data from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample, together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. They concluded that there was highly statistically significant evidence of violations of the strong equivalence principle in weak gravitational fields in the vicinity of rotationally supported galaxies.^[85] They observed an effect inconsistent with tidal effects in the ΛCDM model. These results have been challenged as failing to consider inaccuracies in the rotation curves and correlations between galaxy properties and clustering strength.^[86] and as inconsistent with similar analysis of other galaxies.^[87]

Cold dark matter discrepancies

Several discrepancies between the predictions of cold dark matter in the ΛCDM model and observations of galaxies and their clustering have arisen. Some of these problems have proposed solutions, but it remains unclear whether they can be solved without abandoning the ΛCDM model.^[88]

Cuspy halo problem

The density distributions of dark matter halos in cold dark matter simulations (at least those that do not include the impact of baryonic feedback) are much more peaked than what is observed in galaxies by investigating their rotation curves.^[89]

Dwarf galaxy problem

Cold dark matter simulations predict large numbers of small dark matter halos, more numerous than the number of small dwarf galaxies that are observed around galaxies like the Milky Way.^[90]

Satellite disk problem

Dwarf galaxies around the Milky Way and Andromeda galaxies are observed to be orbiting in thin, planar structures whereas the simulations predict that they should be distributed randomly about their parent galaxies.^[91] However, latest research suggests this seemingly bizarre alignment is just a quirk which will dissolve over time.^[92]

High-velocity galaxy problem

Galaxies in the NGC 3109 association are moving away too rapidly to be consistent with expectations in the ΛCDM model.^[93] In this framework, NGC 3109 is too massive and distant from the Local Group for it to have been flung out in a three-body interaction involving the Milky Way or Andromeda Galaxy.^[94]

Galaxy morphology problem

If galaxies grew hierarchically, then massive galaxies required many mergers. Major mergers inevitably create a classical bulge. On the contrary, about 80 % of observed galaxies give evidence of no such bulges, and giant pure-disc galaxies are commonplace.^[95] The tension can be quantified by comparing the observed distribution of galaxy shapes today with predictions from high-resolution hydrodynamical cosmological simulations in the ΛCDM framework, revealing a highly significant problem that is unlikely to be solved by improving the resolution of the simulations.^[96] The high bulgeless fraction was nearly constant for 8 billion years.^[97]

Fast galaxy bar problem

If galaxies were embedded within massive halos of cold dark matter, then the bars that often develop in their central regions would be slowed down by dynamical friction with the halo. This is in serious tension with the fact that observed galaxy bars are typically fast.^[98]

Small scale crisis

Comparison of the model with observations may have some problems on sub-galaxy scales, possibly predicting too many dwarf galaxies and too much dark matter in the innermost regions of galaxies. This problem is called the "small scale crisis".^[99] These small scales are harder to resolve in computer simulations, so it is not yet clear whether the problem is the simulations, non-standard properties of dark matter, or a more radical error in the model.

High redshift galaxies

Observations from the James Webb Space Telescope have resulted in various galaxies confirmed by spectroscopy at high redshift, such as JADES-GS-z13-0 at cosmological redshift of 13.2.^[100]^[101] Other candidate galaxies which have not been confirmed by spectroscopy include CEERS-93316 at cosmological redshift of 16.4.

Existence of surprisingly massive galaxies in the early universe challenges the preferred models describing how dark matter halos drive galaxy formation. It remains to be seen whether a revision of the Lambda-CDM model with parameters given by Planck Collaboration is necessary to resolve this issue. The discrepancies could also be explained by particular properties (stellar masses or effective volume) of the candidate galaxies, yet unknown force or particle outside of the Standard Model through which dark matter interacts, more efficient baryonic matter accumulation by the dark matter halos, early dark energy models,^[102] or the hypothesized long-sought Population III stars.^[103]^[104]^[105]^[106]

Missing baryon problem

Massimo Persic and Paolo Salucci^[107] first estimated the baryonic density today present in ellipticals, spirals, groups and clusters of galaxies. They performed an integration of the baryonic mass-to-light ratio over luminosity (in the following ${\textstyle M_{\rm {b}}/L}$ ), weighted with the luminosity function ${\textstyle \phi (L)}$ over the previously mentioned classes of astrophysical objects:

\rho _{\rm {b}}=\sum \int L\phi (L){\frac {M_{\rm {b}}}{L}}\,dL.

The result was:

\Omega _{\rm {b}}=\Omega _{*}+\Omega _{\text{gas}}=2.2\times 10^{-3}+1.5\times 10^{-3}\;h^{-1.3}\simeq 0.003,

where $h\simeq 0.72$ .

Note that this value is much lower than the prediction of standard cosmic nucleosynthesis $\Omega _{\rm {b}}\simeq 0.0486$ , so that stars and gas in galaxies and in galaxy groups and clusters account for less than 10 % of the primordially synthesized baryons. This issue is known as the problem of the "missing baryons".

The missing baryon problem is claimed to be resolved. Using observations of the kinematic Sunyaev–Zel'dovich effect spanning more than 90 % of the lifetime of the Universe, in 2021 astrophysicists found that approximately 50 % of all baryonic matter is outside dark matter haloes, filling the space between galaxies.^[108] Together with the amount of baryons inside galaxies and surrounding them, the total amount of baryons in the late time Universe is compatible with early Universe measurements.

Unfalsifiability

It has been argued that the ΛCDM model is built upon a foundation of conventionalist stratagems, rendering it unfalsifiable in the sense defined by Karl Popper.^[109]

Remove ads

More information

,

...

Planck Collaboration Cosmological parameters^[111]
	Description	Symbol	Value-2015^[112]	Value-2018^[113]
Independent parameters	Physical baryon density parameter^[a]	Ω_b `h`²	0.02230±0.00014	0.0224±0.0001
	Physical dark matter density parameter^[a]	Ω_c `h`²	0.1188±0.0010	0.120±0.001
	Age of the universe	`t`₀	(13.799±0.021)×10⁹ years	(13.787±0.020)×10⁹ years^[116]
	Scalar spectral index	`n`_s	0.9667±0.0040	0.965±0.004
	Curvature fluctuation amplitude, `k`₀ = 0.002 Mpc⁻¹	$\Delta _{R}^{2}$	2.441+0.088 −0.092×10⁻⁹^[117]	?
	Reionization optical depth	`τ`	0.066±0.012	0.054±0.007
Fixed parameters	Total density parameter^[b]	Ω_tot	1	?
	Equation of state of dark energy	`w`	−1	w₀ = −1.03 ± 0.03
	Tensor/scalar ratio	`r`	0	r_0.002 < 0.06
	Running of spectral index	$dn_{\text{s}}/d\ln k$	0	?
	Sum of three neutrino masses	$\sum m_{\nu }$	0.06 eV/`c`²^[c]^[110]^: 40	0.12 eV/`c`²
	Effective number of relativistic degrees of freedom	N_eff	3.046^[d]^[110]^: 47	2.99±0.17
Calculated Value	Hubble constant	`H`₀	67.74±0.46 km⋅s⁻¹⋅Mpc⁻¹	67.4±0.5 km⋅s⁻¹⋅Mpc⁻¹
	Baryon density parameter^[b]	Ω_b	0.0486±0.0010^[e]	?
	Dark matter density parameter^[b]	Ω_c	0.2589±0.0057^[f]	?
	Matter density parameter^[b]	Ω_m	0.3089±0.0062	0.315±0.007
	Dark energy density parameter^[b]	Ω_Λ	0.6911±0.0062	0.6847±0.0073
	Critical density	`ρ`_crit	(8.62±0.12)×10⁻²⁷ kg/m³^[g]	?
	The present root-mean-square matter fluctuation, averaged over a sphere of radius 8h⁻¹ Mpc	`σ`₈	0.8159±0.0086	0.811±0.006
	Redshift at decoupling	`z`_∗	1089.90±0.23	1089.80±0.21
	Age at decoupling	`t`_∗	377700±3200 years^[117]	?
	Redshift of reionization (with uniform prior)	`z`_re	8.5+1.0 −1.1^[118]	7.68±0.79

Close

The simple ΛCDM model is based on six parameters: physical baryon density parameter; physical dark matter density parameter; the age of the universe; scalar spectral index; curvature fluctuation amplitude; and reionization optical depth.^[119] In accordance with Occam's razor, six is the smallest number of parameters needed to give an acceptable fit to the observations; other possible parameters are fixed at "natural" values, e.g. total density parameter = 1.00, dark energy equation of state = −1. (See below for extended models that allow these to vary.)

The values of these six parameters are mostly not predicted by theory (though, ideally, they may be related by a future "Theory of Everything"), except that most versions of cosmic inflation predict the scalar spectral index should be slightly smaller than 1, consistent with the estimated value 0.96. The parameter values, and uncertainties, are estimated using large computer searches to locate the region of parameter space providing an acceptable match to cosmological observations. From these six parameters, the other model values, such as the Hubble constant and the dark energy density, can be readily calculated.

Commonly, the set of observations fitted includes the cosmic microwave background anisotropy, the brightness/redshift relation for supernovae, and large-scale galaxy clustering including the baryon acoustic oscillation feature. Other observations, such as the Hubble constant, the abundance of galaxy clusters, weak gravitational lensing and globular cluster ages, are generally consistent with these, providing a check of the model, but are less precisely measured at present.

Parameter values listed in the table are from the Planck Collaboration Cosmological parameters 68 % confidence limits for the base ΛCDM model from Planck CMB power spectra, in combination with lensing reconstruction and external data (BAO + JLA + H₀).^[110] See also Planck (spacecraft).

The "physical baryon density parameter" Ω_b h² is the "baryon density parameter" Ω_b multiplied by the square of the reduced Hubble constant h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).^[114]^[115] Likewise for the difference between "physical dark matter density parameter" and "dark matter density parameter".
A density ρ_x = Ω_xρ_crit is expressed in terms of the critical density ρ_crit, which is the total density of matter/energy needed for the universe to be spatially flat. Measurements indicate that the actual total density ρ_tot is very close if not equal to this value, see below.
This is the minimal value allowed by solar and terrestrial neutrino oscillation experiments.
from the Standard Model of particle physics
Calculated from Ω_bh² and h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).
Calculated from Ω_ch² and h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).
Calculated from h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹) per ρ_crit = 1.87847×10⁻²⁶ h²⋅kg⋅m⁻³.^[15]

Remove ads

More information

,

...

Extended model parameters^[117]
Description	Symbol	Value
Total density parameter	$\Omega _{\text{tot}}$	0.9993±0.0019^[120]
Equation of state of dark energy	$w$	−0.980±0.053
Tensor-to-scalar ratio	$r$	< 0.11, `k`₀ = 0.002 Mpc⁻¹ ( $2\sigma$ )
Running of the spectral index	$dn_{s}/d\ln k$	−0.022±0.020, `k`₀ = 0.002 Mpc⁻¹
Sum of three neutrino masses	$\sum m_{\nu }$	< 0.58 eV/`c`² ( $2\sigma$ )
Physical neutrino density parameter	$\Omega _{\nu }h^{2}$	< 0.0062

Close

Extended models allow one or more of the "fixed" parameters above to vary, in addition to the basic six; so these models join smoothly to the basic six-parameter model in the limit that the additional parameter(s) approach the default values. For example, possible extensions of the simplest ΛCDM model allow for spatial curvature ( $\Omega _{\text{tot}}$ may be different from 1); or quintessence rather than a cosmological constant where the equation of state of dark energy is allowed to differ from −1. Cosmic inflation predicts tensor fluctuations (gravitational waves). Their amplitude is parameterized by the tensor-to-scalar ratio (denoted $r$ ), which is determined by the unknown energy scale of inflation. Other modifications allow hot dark matter in the form of neutrinos more massive than the minimal value, or a running spectral index; the latter is generally not favoured by simple cosmic inflation models.

Allowing additional variable parameter(s) will generally increase the uncertainties in the standard six parameters quoted above, and may also shift the central values slightly. The table below shows results for each of the possible "6+1" scenarios with one additional variable parameter; this indicates that, as of 2015, there is no convincing evidence that any additional parameter is different from its default value.

Some researchers have suggested that there is a running spectral index, but no statistically significant study has revealed one. Theoretical expectations suggest that the tensor-to-scalar ratio $r$ should be between 0 and 0.3, and the latest results are within those limits.

Remove ads

Bolshoi cosmological simulation
Galaxy formation and evolution
Illustris project
List of cosmological computation software
Millennium Run
Weakly interacting massive particles (WIMPs)
The ΛCDM model is also known as the standard model of cosmology, but is not related to the Standard Model of particle physics.

[1]
Deruelle, Nathalie; Uzan, Jean-Philippe (2018-08-30). de Forcrand-Millard, Patricia (ed.). Relativity in Modern Physics (1 ed.). Oxford University Press. doi:10.1093/oso/9780198786399.001.0001. ISBN 978-0-19-878639-9.
[2]
Maeder, Andre (2017). "An Alternative to the ΛCDM Model: The Case of Scale Invariance". The Astrophysical Journal. 834 (2): 194. arXiv:1701.03964. Bibcode:2017ApJ...834..194M. doi:10.3847/1538-4357/834/2/194. ISSN 0004-637X. S2CID 119513478.
[3]
Brouwer, Margot (2017). "First test of Verlinde's theory of emergent gravity using weak gravitational lensing measurements". Monthly Notices of the Royal Astronomical Society. 466 (3): 2547–2559. arXiv:1612.03034. Bibcode:2017MNRAS.466.2547B. doi:10.1093/mnras/stw3192. S2CID 18916375.
[4]
P. Kroupa, B. Famaey, K.S. de Boer, J. Dabringhausen, M. Pawlowski, C.M. Boily, H. Jerjen, D. Forbes, G. Hensler, M. Metz, "Local-Group tests of dark-matter concordance cosmology. Towards a new paradigm for structure formation" A&A 523, 32 (2010).
[5]
Petit, J. P.; D'Agostini, G. (2018-07-01). "Constraints on Janus Cosmological model from recent observations of supernovae type Ia". Astrophysics and Space Science. 363 (7): 139. Bibcode:2018Ap&SS.363..139D. doi:10.1007/s10509-018-3365-3. ISSN 1572-946X. S2CID 125167116.
[6]
Pandey, Kanhaiya L.; Karwal, Tanvi; Das, Subinoy (2019-10-21). "Alleviating the H0 and S8 Anomalies With a Decaying Dark Matter Model". Journal of Cosmology and Astroparticle Physics. arXiv:1902.10636. doi:10.1088/1475-7516/2020/07/026. S2CID 119234939.
[7]
Davis, Tamara M.; Lineweaver, Charles H. (2004). "Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe". Publications of the Astronomical Society of Australia. 21 (1): 97–109. arXiv:astro-ph/0310808. Bibcode:2004PASA...21...97D. doi:10.1071/AS03040. ISSN 1323-3580.
[8]
DES Collaboration (2018). "First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters". The Astrophysical Journal. 872 (2): L30. arXiv:1811.02374. Bibcode:2019ApJ...872L..30A. doi:10.3847/2041-8213/ab04fa. S2CID 84833144.
[9]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641: A6. arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.
[10]
Persic, M.; et al. (1996). "The universal rotation curve of spiral galaxies — I. The dark matter connection". Monthly Notices of the Royal Astronomical Society. 281 (1): 27–47. arXiv:astro-ph/9506004. Bibcode:1996MNRAS.281...27P. doi:10.1093/mnras/278.1.27.
[11]
Bertone, Gianfranco; Hooper, Dan (2018-10-15). "History of dark matter". Reviews of Modern Physics. 90 (4): 045002. arXiv:1605.04909. Bibcode:2018RvMP...90d5002B. doi:10.1103/RevModPhys.90.045002. ISSN 0034-6861.
[12]
Tanabashi, M.; et al. (Particle Data Group) (2019). "Astrophysical Constants and Parameters" (PDF). Physical Review D. 98 (3). Particle Data Group: 030001. Bibcode:2018PhRvD..98c0001T. doi:10.1103/PhysRevD.98.030001. Retrieved 2020-03-08.
[13]
Persic, Massimo; Salucci, Paolo (1992-09-01). "The baryon content of the Universe". Monthly Notices of the Royal Astronomical Society. 258 (1): 14P–18P. arXiv:astro-ph/0502178. Bibcode:1992MNRAS.258P..14P. doi:10.1093/mnras/258.1.14P. ISSN 0035-8711. S2CID 17945298.
[14]
Dodelson, Scott (2008). Modern cosmology (4 ed.). San Diego, CA: Academic Press. ISBN 978-0-12-219141-1.
[15]
K.A. Olive; et al. (Particle Data Group) (2015). "The Review of Particle Physics. 2. Astrophysical constants and parameters" (PDF). Particle Data Group: Berkeley Lab. Archived from the original (PDF) on 3 December 2015. Retrieved 10 January 2016.
[16]
Frieman, Joshua A.; Turner, Michael S.; Huterer, Dragan (2008). "Dark Energy and the Accelerating Universe". Annual Review of Astronomy and Astrophysics. 46 (1): 385–432. arXiv:0803.0982. Bibcode:2008ARA&A..46..385F. doi:10.1146/annurev.astro.46.060407.145243. S2CID 15117520.
[17]
Elcio Abdalla; Guillermo Franco Abellán; et al. (11 Mar 2022). "Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies". Journal of High Energy Astrophysics. 34: 49. arXiv:2203.06142v1. Bibcode:2022JHEAp..34...49A. doi:10.1016/j.jheap.2022.04.002. S2CID 247411131.
[18]
Matthew Chalmers (2 July 2021). "Exploring the Hubble tension". CERN Courier. Retrieved 25 March 2022.
[19]
Kovac, J. M.; Leitch, E. M.; Pryke, C.; Carlstrom, J. E.; Halverson, N. W.; Holzapfel, W. L. (2002). "Detection of polarization in the cosmic microwave background using DASI". Nature. 420 (6917): 772–787. arXiv:astro-ph/0209478. Bibcode:2002Natur.420..772K. doi:10.1038/nature01269. PMID 12490941. S2CID 4359884.
[20]
Planck Collaboration (2016). "Planck 2015 Results. XIII. Cosmological Parameters". Astronomy & Astrophysics. 594 (13): A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.
[21]
Michael Turner (12 Jan 2022). "The Road to Precision Cosmology". Annual Review of Nuclear and Particle Science. 32: 1–35. arXiv:2201.04741. Bibcode:2022ARNPS..72....1T. doi:10.1146/annurev-nucl-111119-041046. S2CID 245906450.
[22]
Andrew Liddle. An Introduction to Modern Cosmology (2nd ed.). London: Wiley, 2003.
[23]
Steven Weinberg (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons, Inc. ISBN 978-0-471-92567-5.
[24]
Jacques Colin; Roya Mohayaee; Mohamed Rameez; Subir Sarkar (20 November 2019). "Evidence for anisotropy of cosmic acceleration". Astronomy and Astrophysics. 631: L13. arXiv:1808.04597. Bibcode:2019A&A...631L..13C. doi:10.1051/0004-6361/201936373. S2CID 208175643. Retrieved 25 March 2022.
[25]
Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble Tension Signal a Breakdown in FLRW Cosmology?". Classical and Quantum Gravity. 38 (18): 184001. arXiv:2105.09790. Bibcode:2021CQGra..38r4001K. doi:10.1088/1361-6382/ac1a81. ISSN 0264-9381. S2CID 234790314.
[26]
Asta Heinesen; Hayley J. Macpherson (15 July 2021). "Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study". Physical Review D. 104 (2): 023525. arXiv:2103.11918. Bibcode:2021PhRvD.104b3525M. doi:10.1103/PhysRevD.104.023525. S2CID 232307363. Retrieved 25 March 2022.
[27]
Ellis, G. F. R. (2009). "Dark energy and inhomogeneity". Journal of Physics: Conference Series. 189 (1): 012011. Bibcode:2009JPhCS.189a2011E. doi:10.1088/1742-6596/189/1/012011. S2CID 250670331.
[28]
Lee Billings (April 15, 2020). "Do We Live in a Lopsided Universe?". Scientific American. Retrieved March 24, 2022.
[29]
Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (8 April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation". Astronomy & Astrophysics. 636 (April 2020): 42. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. S2CID 215238834. Retrieved 24 March 2022.
[30]
Nathan J. Secrest; Sebastian von Hausegger; Mohamed Rameez; Roya Mohayaee; Subir Sarkar; Jacques Colin (February 25, 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal Letters. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. S2CID 222066749.
[31]
B. Javanmardi; C. Porciani; P. Kroupa; J. Pflamm-Altenburg (August 27, 2015). "Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae". The Astrophysical Journal Letters. 810 (1): 47. arXiv:1507.07560. Bibcode:2015ApJ...810...47J. doi:10.1088/0004-637X/810/1/47. S2CID 54958680. Retrieved March 24, 2022.
[32]
"Simple but challenging: the Universe according to Planck". ESA Science & Technology. October 5, 2016 [March 21, 2013]. Retrieved October 29, 2016.
[33]
Dennis Sciama (12 June 1967). "Peculiar Velocity of the Sun and the Cosmic Microwave Background". Physical Review Letters. 18 (24): 1065–1067. Bibcode:1967PhRvL..18.1065S. doi:10.1103/PhysRevLett.18.1065. Retrieved 25 March 2022.
[34]
G. F. R. Ellis; J. E. Baldwin (1 January 1984). "On the expected anisotropy of radio source counts". Monthly Notices of the Royal Astronomical Society. 206 (2): 377–381. doi:10.1093/mnras/206.2.377. Retrieved 25 March 2022.
[35]
Siewert, Thilo M.; Schmidt-Rubart, Matthias; Schwarz, Dominik J. (2021). "Cosmic radio dipole: Estimators and frequency dependence". Astronomy & Astrophysics. 653: A9. arXiv:2010.08366. Bibcode:2021A&A...653A...9S. doi:10.1051/0004-6361/202039840. S2CID 223953708.
[36]
Secrest, Nathan; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (25 February 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. ISSN 2041-8213. S2CID 222066749.
[37]
Singal, Ashok K. (2022). "Peculiar motion of Solar system from the Hubble diagram of supernovae Ia and its implications for cosmology". Monthly Notices of the Royal Astronomical Society. 515 (4): 5969–5980. arXiv:2106.11968. doi:10.1093/mnras/stac1986.
[38]
Singal, Ashok K. (2022). "Solar system peculiar motion from the Hubble diagram of quasars and testing the cosmological principle". Monthly Notices of the Royal Astronomical Society. 511 (2): 1819–1829. arXiv:2107.09390. doi:10.1093/mnras/stac144.
[39]
de Oliveira-Costa, Angelica; Tegmark, Max; Zaldarriaga, Matias; Hamilton, Andrew (25 March 2004). "The significance of the largest scale CMB fluctuations in WMAP". Physical Review D. 69 (6): 063516. arXiv:astro-ph/0307282. Bibcode:2004PhRvD..69f3516D. doi:10.1103/PhysRevD.69.063516. ISSN 1550-7998. S2CID 119463060.
[40]
Land, Kate; Magueijo, Joao (28 November 2005). "Is the Universe odd?". Physical Review D. 72 (10): 101302. arXiv:astro-ph/0507289. Bibcode:2005PhRvD..72j1302L. doi:10.1103/PhysRevD.72.101302. ISSN 1550-7998. S2CID 119333704.
[41]
Kim, Jaiseung; Naselsky, Pavel (10 May 2010). "Anomalous parity asymmetry of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles". The Astrophysical Journal. 714 (2): L265–L267. arXiv:1001.4613. Bibcode:2010ApJ...714L.265K. doi:10.1088/2041-8205/714/2/L265. ISSN 2041-8205. S2CID 24389919.
[42]
Hutsemekers, D.; Cabanac, R.; Lamy, H.; Sluse, D. (October 2005). "Mapping extreme-scale alignments of quasar polarization vectors". Astronomy & Astrophysics. 441 (3): 915–930. arXiv:astro-ph/0507274. Bibcode:2005A&A...441..915H. doi:10.1051/0004-6361:20053337. ISSN 0004-6361. S2CID 14626666.
[43]
Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the $L_{\text{X}}-T$ scaling relation". Astronomy & Astrophysics. 636: A15. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. ISSN 0004-6361. S2CID 215238834.
[44]
Migkas, K.; Pacaud, F.; Schellenberger, G.; Erler, J.; Nguyen-Dang, N. T.; Reiprich, T. H.; Ramos-Ceja, M. E.; Lovisari, L. (May 2021). "Cosmological implications of the anisotropy of ten galaxy cluster scaling relations". Astronomy & Astrophysics. 649: A151. arXiv:2103.13904. Bibcode:2021A&A...649A.151M. doi:10.1051/0004-6361/202140296. ISSN 0004-6361. S2CID 232352604.
[45]
Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (2022). "Hints of FLRW breakdown from supernovae". Physical Review D. 105 (6): 063514. arXiv:2106.02532. Bibcode:2022PhRvD.105f3514K. doi:10.1103/PhysRevD.105.063514. S2CID 235352881.
[46]
Luongo, Orlando; Muccino, Marco; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (2022). "Larger H0 values in the CMB dipole direction". Physical Review D. 105 (10): 103510. arXiv:2108.13228. Bibcode:2022PhRvD.105j3510L. doi:10.1103/PhysRevD.105.103510. S2CID 248713777.
[47]
Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen, JD (2016). "How Isotropic is the Universe?". Physical Review Letters. 117 (13): 131302. arXiv:1605.07178. Bibcode:2016PhRvL.117m1302S. doi:10.1103/PhysRevLett.117.131302. PMID 27715088. S2CID 453412.
[48]
Yadav, Jaswant; J. S. Bagla; Nishikanta Khandai (25 February 2010). "Fractal dimension as a measure of the scale of homogeneity". Monthly Notices of the Royal Astronomical Society. 405 (3): 2009–2015. arXiv:1001.0617. Bibcode:2010MNRAS.405.2009Y. doi:10.1111/j.1365-2966.2010.16612.x. S2CID 118603499.
[49]
Gott, J. Richard III; et al. (May 2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484. arXiv:astro-ph/0310571. Bibcode:2005ApJ...624..463G. doi:10.1086/428890. S2CID 9654355.
[50]
Horvath, I.; Hakkila, J.; Bagoly, Z. (2013). "The largest structure of the Universe, defined by Gamma-Ray Bursts". arXiv:1311.1104 [astro-ph.CO].
[51]
"Line of galaxies is so big it breaks our understanding of the universe".
[52]
Cooper, Keith (22 January 2024). "An impossibly huge ring of galaxies might lead us to new physics. Here's how". Space.com. Retrieved 31 January 2024.
[53]
Nadathur, Seshadri (2013). "Seeing patterns in noise: gigaparsec-scale 'structures' that do not violate homogeneity". Monthly Notices of the Royal Astronomical Society. 434 (1): 398–406. arXiv:1306.1700. Bibcode:2013MNRAS.434..398N. doi:10.1093/mnras/stt1028. S2CID 119220579.
[54]
Asencio, E; Banik, I; Kroupa, P (2021-02-21). "A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology". Monthly Notices of the Royal Astronomical Society. 500 (2): 5249–5267. arXiv:2012.03950. Bibcode:2021MNRAS.500.5249A. doi:10.1093/mnras/staa3441. ISSN 0035-8711.
[55]
Asencio, E; Banik, I; Kroupa, P (2023-09-10). "A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology". The Astrophysical Journal. 954 (2): 162. arXiv:2308.00744. Bibcode:2023ApJ...954..162A. doi:10.3847/1538-4357/ace62a. ISSN 1538-4357.
[56]
Katz, H; McGaugh, S; Teuben, P; Angus, G. W. (2013-07-20). "Galaxy Cluster Bulk Flows and Collision Velocities in QUMOND". The Astrophysical Journal. 772 (1): 10. arXiv:1305.3651. Bibcode:2013ApJ...772...10K. doi:10.1088/0004-637X/772/1/10. ISSN 1538-4357.
[57]
Keenan, Ryan C.; Barger, Amy J.; Cowie, Lennox L. (2013). "Evidence for a ~300 Mpc Scale Under-density in the Local Galaxy Distribution". The Astrophysical Journal. 775 (1): 62. arXiv:1304.2884. Bibcode:2013ApJ...775...62K. doi:10.1088/0004-637X/775/1/62. S2CID 118433293.
[58]
Siegel, Ethan. "We're Way Below Average! Astronomers Say Milky Way Resides In A Great Cosmic Void". Forbes. Retrieved 2017-06-09.
[59]
Haslbauer, M; Banik, I; Kroupa, P (2020-12-21). "The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution". Monthly Notices of the Royal Astronomical Society. 499 (2): 2845–2883. arXiv:2009.11292. Bibcode:2020MNRAS.499.2845H. doi:10.1093/mnras/staa2348. ISSN 0035-8711.
[60]
Sahlén, Martin; Zubeldía, Íñigo; Silk, Joseph (2016). "Cluster–Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void". The Astrophysical Journal Letters. 820 (1): L7. arXiv:1511.04075. Bibcode:2016ApJ...820L...7S. doi:10.3847/2041-8205/820/1/L7. ISSN 2041-8205. S2CID 119286482.
[61]
di Valentino, Eleonora; Mena, Olga; Pan, Supriya; et al. (2021). "In the realm of the Hubble tension—a review of solutions". Classical and Quantum Gravity. 38 (15): 153001. arXiv:2103.01183. Bibcode:2021CQGra..38o3001D. doi:10.1088/1361-6382/ac086d. S2CID 232092525.
[62]
Mann, Adam (26 August 2019). "One Number Shows Something Is Fundamentally Wrong with Our Conception of the Universe – This fight has universal implications". Live Science. Retrieved 26 August 2019.
[63]
Gresko, Michael (17 December 2021). "The universe is expanding faster than it should be". nationalgeographic.com. National Geographic. Archived from the original on December 17, 2021. Retrieved 21 December 2021.
[64]
Shanks, T; Hogarth, L M; Metcalfe, N (2019-03-21). "Gaia Cepheid parallaxes and 'Local Hole' relieve H 0 tension". Monthly Notices of the Royal Astronomical Society: Letters. 484 (1): L64–L68. arXiv:1810.02595. Bibcode:2019MNRAS.484L..64S. doi:10.1093/mnrasl/sly239. ISSN 1745-3925.
[65]
Kenworthy, W. D'Arcy; Scolnic, Dan; Riess, Adam (2019-04-24). "The Local Perspective on the Hubble Tension: Local Structure Does Not Impact Measurement of the Hubble Constant". The Astrophysical Journal. 875 (2): 145. arXiv:1901.08681. Bibcode:2019ApJ...875..145K. doi:10.3847/1538-4357/ab0ebf. ISSN 1538-4357. S2CID 119095484.
[66]
Poulin, Vivian; Smith, Tristan L.; Karwal, Tanvi; Kamionkowski, Marc (2019-06-04). "Early Dark Energy can Resolve the Hubble Tension". Physical Review Letters. 122 (22): 221301. arXiv:1811.04083. Bibcode:2019PhRvL.122v1301P. doi:10.1103/PhysRevLett.122.221301. PMID 31283280. S2CID 119233243.
[67]
Planck Collaboration; Aghanim, N.; Akrami, Y.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Basak, S.; Battye, R.; Benabed, K.; Bernard, J.-P.; Bersanelli, M. (September 2020). "Planck 2018 results: VI. Cosmological parameters (Corrigendum)". Astronomy & Astrophysics. 652: C4. doi:10.1051/0004-6361/201833910e. hdl:10902/24951. ISSN 0004-6361.
[68]
Heymans, Catherine; Tröster, Tilman; Asgari, Marika; Blake, Chris; Hildebrandt, Hendrik; Joachimi, Benjamin; Kuijken, Konrad; Lin, Chieh-An; Sánchez, Ariel G.; van den Busch, Jan Luca; Wright, Angus H.; Amon, Alexandra; Bilicki, Maciej; de Jong, Jelte; Crocce, Martin (February 2021). "KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints". Astronomy & Astrophysics. 646: A140. arXiv:2007.15632. Bibcode:2021A&A...646A.140H. doi:10.1051/0004-6361/202039063. ISSN 0004-6361.
[69]
Wood, Charlie (8 September 2020). "A New Cosmic Tension: The Universe Might Be Too Thin". Quanta Magazine.
[70]
Abbott, T. M. C.; Aguena, M.; Alarcon, A.; Allam, S.; Alves, O.; Amon, A.; Andrade-Oliveira, F.; Annis, J.; Avila, S.; Bacon, D.; Baxter, E.; Bechtol, K.; Becker, M. R.; Bernstein, G. M.; Bhargava, S. (2022-01-13). "Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing". Physical Review D. 105 (2): 023520. arXiv:2105.13549. Bibcode:2022PhRvD.105b3520A. doi:10.1103/PhysRevD.105.023520. hdl:11368/3013060. ISSN 2470-0010.
[71]
Dark Energy Survey; Kilo-Degree Survey Collaboration; Abbott, T.M.C.; Aguena, M.; Alarcon, A.; Alves, O.; Amon, A.; Andrade-Oliveira, F.; Asgari, M.; Avila, S.; Bacon, D.; Bechtol, K.; Becker, M. R.; Bernstein, G. M.; Bertin, E. (2023-10-20). "DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys". The Open Journal of Astrophysics. 6: 36. arXiv:2305.17173. Bibcode:2023OJAp....6E..36D. doi:10.21105/astro.2305.17173. ISSN 2565-6120.
[72]
Li, Xiangchong; Zhang, Tianqing; Sugiyama, Sunao; Dalal, Roohi; Terasawa, Ryo; Rau, Markus M.; Mandelbaum, Rachel; Takada, Masahiro; More, Surhud; Strauss, Michael A.; Miyatake, Hironao; Shirasaki, Masato; Hamana, Takashi; Oguri, Masamune; Luo, Wentao (2023-12-11). "Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions". Physical Review D. 108 (12): 123518. arXiv:2304.00702. Bibcode:2023PhRvD.108l3518L. doi:10.1103/PhysRevD.108.123518. ISSN 2470-0010.
[73]
Dalal, Roohi; Li, Xiangchong; Nicola, Andrina; Zuntz, Joe; Strauss, Michael A.; Sugiyama, Sunao; Zhang, Tianqing; Rau, Markus M.; Mandelbaum, Rachel; Takada, Masahiro; More, Surhud; Miyatake, Hironao; Kannawadi, Arun; Shirasaki, Masato; Taniguchi, Takanori (2023-12-11). "Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra". Physical Review D. 108 (12): 123519. arXiv:2304.00701. Bibcode:2023PhRvD.108l3519D. doi:10.1103/PhysRevD.108.123519. ISSN 2470-0010.
[74]
Yoon, Mijin (2023-12-11). "Inconsistency Turns Up Again for Cosmological Observations". Physics. 16 (12): 193. arXiv:2304.00701. Bibcode:2023PhRvD.108l3519D. doi:10.1103/PhysRevD.108.123519.
[75]
Kruesi, Liz (19 January 2024). "Clashing Cosmic Numbers Challenge Our Best Theory of the Universe". Quanta Magazine.
[76]
Ghirardini, V.; Bulbul, E.; Artis, E.; Clerc, N.; Garrel, C.; Grandis, S.; Kluge, M.; Liu, A.; Bahar, Y. E.; Balzer, F.; Chiu, I.; Comparat, J.; Gruen, D.; Kleinebreil, F.; Krippendorf, S. (February 2024). "The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic Hemisphere". arXiv:2402.08458 [astro-ph.CO].
[77]
Kruesi, Liz (4 March 2024). "Fresh X-Rays Reveal a Universe as Clumpy as Cosmology Predicts". Quanta Magazine.
[78]
Said, Khaled; Colless, Matthew; Magoulas, Christina; Lucey, John R; Hudson, Michael J (2020-09-01). "Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity". Monthly Notices of the Royal Astronomical Society. 497 (1): 1275–1293. arXiv:2007.04993. doi:10.1093/mnras/staa2032. ISSN 0035-8711.
[79]
Boruah, Supranta S; Hudson, Michael J; Lavaux, Guilhem (2020-09-21). "Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints". Monthly Notices of the Royal Astronomical Society. 498 (2): 2703–2718. arXiv:1912.09383. doi:10.1093/mnras/staa2485. ISSN 0035-8711.
[80]
[81]
[82]
Fields, B. D. (2011). "The primordial lithium problem". Annual Review of Nuclear and Particle Science. 61 (1): 47–68. arXiv:1203.3551. Bibcode:2011ARNPS..61...47F. doi:10.1146/annurev-nucl-102010-130445.
[83]
Eleonora Di Valentino; Alessandro Melchiorri; Joseph Silk (4 November 2019). "Planck evidence for a closed Universe and a possible crisis for cosmology". Nature Astronomy. 4 (2): 196–203. arXiv:1911.02087. doi:10.1038/s41550-019-0906-9. S2CID 207880880. Retrieved 24 March 2022.
[84]
Philip Bull; Marc Kamionkowski (15 April 2013). "What if Planck's Universe isn't flat?". Physical Review D. 87 (3): 081301. arXiv:1302.1617. Bibcode:2013PhRvD..87h1301B. doi:10.1103/PhysRevD.87.081301. S2CID 118437535. Retrieved 24 March 2022.
[85]
Chae, Kyu-Hyun; Lelli, Federico; Desmond, Harry; McGaugh, Stacy S.; Li, Pengfei; Schombert, James M. (2020). "Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies". The Astrophysical Journal. 904 (1): 51. arXiv:2009.11525. Bibcode:2020ApJ...904...51C. doi:10.3847/1538-4357/abbb96. S2CID 221879077.
[86]
Paranjape, Aseem; Sheth, Ravi K (2022-10-04). "The phenomenology of the external field effect in cold dark matter models". Monthly Notices of the Royal Astronomical Society. 517 (1): 130–139. arXiv:2112.00026. doi:10.1093/mnras/stac2689. ISSN 0035-8711.
[87]
Freundlich, Jonathan; Famaey, Benoit; Oria, Pierre-Antoine; Bílek, Michal; Müller, Oliver; Ibata, Rodrigo (2022-02-01). "Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies". Astronomy & Astrophysics. 658: A26. arXiv:2109.04487. Bibcode:2022A&A...658A..26F. doi:10.1051/0004-6361/202142060. ISSN 0004-6361. We hence do not see any evidence for a violation of the strong equivalence principle in Coma cluster UDGs, contrarily to, for instance, Chae et al. (2020, 2021), for disc galaxies in the field. Our work extends that of Bílek et al. (2019b) and Haghi et al. (2019a), which is limited to DF44 and makes the result all the more compelling. We recall that the MOND predictions do not involve any free parameter.
[88]
Kroupa, P.; Famaey, B.; de Boer, Klaas S.; Dabringhausen, Joerg; Pawlowski, Marcel; Boily, Christian; Jerjen, Helmut; Forbes, Duncan; Hensler, Gerhard (2010). "Local-Group tests of dark-matter Concordance Cosmology: Towards a new paradigm for structure formation". Astronomy and Astrophysics. 523: 32–54. arXiv:1006.1647. Bibcode:2010A&A...523A..32K. doi:10.1051/0004-6361/201014892. S2CID 11711780.
[89]
Gentile, G.; Salucci, P. (2004). "The cored distribution of dark matter in spiral galaxies". Monthly Notices of the Royal Astronomical Society. 351 (3): 903–922. arXiv:astro-ph/0403154. Bibcode:2004MNRAS.351..903G. doi:10.1111/j.1365-2966.2004.07836.x. S2CID 14308775.
[90]
Klypin, Anatoly; Kravtsov, Andrey V.; Valenzuela, Octavio; Prada, Francisco (1999). "Where are the missing galactic satellites?". Astrophysical Journal. 522 (1): 82–92. arXiv:astro-ph/9901240. Bibcode:1999ApJ...522...82K. doi:10.1086/307643. S2CID 12983798.
[91]
Pawlowski, Marcel; et al. (2014). "Co-orbiting satellite galaxy structures are still in conflict with the distribution of primordial dwarf galaxies". Monthly Notices of the Royal Astronomical Society. 442 (3): 2362–2380. arXiv:1406.1799. Bibcode:2014MNRAS.442.2362P. doi:10.1093/mnras/stu1005.
[92]
Sawala, Till; Cautun, Marius; Frenk, Carlos; et al. (2022). "The Milky Way's plane of satellites: consistent with ΛCDM". Nature Astronomy. 7 (4): 481–491. arXiv:2205.02860. Bibcode:2023NatAs...7..481S. doi:10.1038/s41550-022-01856-z. S2CID 254920916.
[93]
Banik, Indranil; Zhao, H (2018-01-21). "A plane of high velocity galaxies across the Local Group". Monthly Notices of the Royal Astronomical Society. 473 (3): 4033–4054. arXiv:1701.06559. Bibcode:2018MNRAS.473.4033B. doi:10.1093/mnras/stx2596. ISSN 0035-8711.
[94]
Banik, Indranil; Haslbauer, Moritz; Pawlowski, Marcel S.; Famaey, Benoit; Kroupa, Pavel (2021-06-21). "On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework". Monthly Notices of the Royal Astronomical Society. 503 (4): 6170–6186. arXiv:2105.04575. Bibcode:2021MNRAS.503.6170B. doi:10.1093/mnras/stab751. ISSN 0035-8711.
[95]
Kormendy, J.; Drory, N.; Bender, R.; Cornell, M.E. (2010). "Bulgeless giant galaxies challenge our picture of galaxy formation by hierarchical clustering". The Astrophysical Journal. 723 (1): 54–80. arXiv:1009.3015. Bibcode:2010ApJ...723...54K. doi:10.1088/0004-637X/723/1/54. S2CID 119303368.
[96]
Haslbauer, M; Banik, I; Kroupa, P; Wittenburg, N; Javanmardi, B (2022-02-01). "The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology". The Astrophysical Journal. 925 (2): 183. arXiv:2202.01221. Bibcode:2022ApJ...925..183H. doi:10.3847/1538-4357/ac46ac. ISSN 1538-4357.
[97]
Sachdeva, S.; Saha, K. (2016). "Survival of pure disk galaxies over the last 8 billion years". The Astrophysical Journal Letters. 820 (1): L4. arXiv:1602.08942. Bibcode:2016ApJ...820L...4S. doi:10.3847/2041-8205/820/1/L4. S2CID 14644377.
[98]
Mahmood, R; Ghafourian, N; Kashfi, T; Banik, I; Haslbauer, M; Cuomo, V; Famaey, B; Kroupa, P (2021-11-01). "Fast galaxy bars continue to challenge standard cosmology". Monthly Notices of the Royal Astronomical Society. 508 (1): 926–939. arXiv:2106.10304. Bibcode:2021MNRAS.508..926R. doi:10.1093/mnras/stab2553. hdl:10023/24680. ISSN 0035-8711.
[99]
Rini, Matteo (2017). "Synopsis: Tackling the Small-Scale Crisis". Physical Review D. 95 (12): 121302. arXiv:1703.10559. Bibcode:2017PhRvD..95l1302N. doi:10.1103/PhysRevD.95.121302. S2CID 54675159.
[100]
Cesari, Thaddeus (9 December 2022). "NASA's Webb Reaches New Milestone in Quest for Distant Galaxies". Retrieved 9 December 2022.
[101]
Curtis-Lake, Emma; et al. (December 2022). "Spectroscopy of four metal-poor galaxies beyond redshift ten" (PDF). arXiv:2212.04568.
[102]
Smith, Tristian L.; Lucca, Matteo; Poulin, Vivian; Abellan, Guillermo F.; Balkenhol, Lennart; Benabed, Karim; Galli, Silvia; Murgia, Riccardo (August 2022). "Hints of early dark energy in Planck, SPT, and ACT data: New physics or systematics?". Physical Review D. 106 (4): 043526. arXiv:2202.09379. Bibcode:2022PhRvD.106d3526S. doi:10.1103/PhysRevD.106.043526. S2CID 247011465.
[103]
Boylan-Kolchin, Michael (2023). "Stress testing ΛCDM with high-redshift galaxy candidates". Nature Astronomy. 7 (6): 731–735. arXiv:2208.01611. Bibcode:2023NatAs...7..731B. doi:10.1038/s41550-023-01937-7. PMC 10281863. PMID 37351007. S2CID 251252960.
[104]
O'Callaghan, Jonathan (6 December 2022). "Astronomers Grapple with JWST's Discovery of Early Galaxies". Scientific American. Retrieved 10 December 2022.
[105]
Behroozi, Peter; Conroy, Charlie; Wechsler, Risa H.; Hearin, Andrew; Williams, Christina C.; Moster, Benjamin P.; Yung, L. Y. Aaron; Somerville, Rachel S.; Gottlöber, Stefan; Yepes, Gustavo; Endsley, Ryan (December 2020). "The Universe at z > 10: predictions for JWST from the UNIVERSEMACHINE DR1". Monthly Notices of the Royal Astronomical Society. 499 (4): 5702–5718. arXiv:2007.04988. Bibcode:2020MNRAS.499.5702B. doi:10.1093/mnras/staa3164.
[106]
Volker Springel; Lars Hernquist (February 2003). "The history of star formation in a Λ cold dark matter universe". Monthly Notices of the Royal Astronomical Society. 339 (2): 312–334. arXiv:astro-ph/0206395. Bibcode:2003MNRAS.339..312S. doi:10.1046/j.1365-8711.2003.06207.x. S2CID 8715136.
[107]
Persic, M.; Salucci, P. (1992-09-01). "The baryon content of the Universe". Monthly Notices of the Royal Astronomical Society. 258 (1): 14P–18P. arXiv:astro-ph/0502178. Bibcode:1992MNRAS.258P..14P. doi:10.1093/mnras/258.1.14P. ISSN 0035-8711.
[108]
Chaves-Montero, Jonás; Hernández-Monteagudo, Carlos; Angulo, Raúl E; Emberson, J D (2021-03-25). "Measuring the evolution of intergalactic gas from z = 0 to 5 using the kinematic Sunyaev–Zel'dovich effect". Monthly Notices of the Royal Astronomical Society. 503 (2): 1798–1814. arXiv:1911.10690. doi:10.1093/mnras/staa3782. ISSN 0035-8711.
[109]
Merritt, David (2017). "Cosmology and convention". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 57: 41–52. arXiv:1703.02389. Bibcode:2017SHPMP..57...41M. doi:10.1016/j.shpsb.2016.12.002. S2CID 119401938.
[110]
Planck Collaboration (2016). "Planck 2015 results. XIII. Cosmological parameters". Astronomy & Astrophysics. 594 (13): A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.
[111]
Planck 2015,^[110] p. 32, table 4, last column.
[112]
Planck 2015,^[110] p. 32, table 4, last column.
[113]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column). arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.
[114]
Appendix A of the LSST Science Book Version 2.0 Archived 2013-02-26 at the Wayback Machine
[115]
p. 7 of Findings of the Joint Dark Energy Mission Figure of Merit Science Working Group
[116]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column). arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.
[117]
Table 8 on p. 39 of Jarosik, N. et al. (WMAP Collaboration) (2011). "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results" (PDF). The Astrophysical Journal Supplement Series. 192 (2): 14. arXiv:1001.4744. Bibcode:2011ApJS..192...14J. doi:10.1088/0067-0049/192/2/14. hdl:2152/43001. S2CID 46171526. Retrieved 2010-12-04. (from NASA's WMAP Documents page)
[118]
Planck Collaboration; Adam, R.; Aghanim, N.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B. (2016-05-11). "Planck intermediate results. XLVII. Planck constraints on reionization history". Astronomy & Astrophysics. 596 (108): A108. arXiv:1605.03507. Bibcode:2016A&A...596A.108P. doi:10.1051/0004-6361/201628897. S2CID 5892152.
[119]
Spergel, D. N. (2015). "The dark side of the cosmology: dark matter and dark energy". Science. 347 (6226): 1100–1102. Bibcode:2015Sci...347.1100S. doi:10.1126/science.aaa0980. PMID 25745164.
[120]
Zyla, P.A.; et al. (Particle Data Group) (2020). "Cosmological Parameters" (PDF). Prog. Theor. Exp. Phys. 083C01.

Ostriker, J. P.; Steinhardt, P. J. (1995). "Cosmic Concordance". arXiv:astro-ph/9505066.
Ostriker, Jeremiah P.; Mitton, Simon (2013). Heart of Darkness: Unraveling the mysteries of the invisible universe. Princeton, NJ: Princeton University Press. ISBN 978-0-691-13430-7.
Rebolo, R.; et al. (2004). "Cosmological parameter estimation using Very Small Array data out to ℓ= 1500". Monthly Notices of the Royal Astronomical Society. 353 (3): 747–759. arXiv:astro-ph/0402466. Bibcode:2004MNRAS.353..747R. doi:10.1111/j.1365-2966.2004.08102.x. S2CID 13971059.

[physical_density-116] The "physical baryon density parameter" Ω_b h² is the "baryon density parameter" Ω_b multiplied by the square of the reduced Hubble constant h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).^[114]^[115] Likewise for the difference between "physical dark matter density parameter" and "dark matter density parameter".

[density-119] A density ρ_x = Ω_xρ_crit is expressed in terms of the critical density ρ_crit, which is the total density of matter/energy needed for the universe to be spatially flat. Measurements indicate that the actual total density ρ_tot is very close if not equal to this value, see below.

[120] This is the minimal value allowed by solar and terrestrial neutrino oscillation experiments.

[121] rom the Standard Model of particle physics

[122] Calculated from Ω_bh² and h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).

[123] Calculated from Ω_ch² and h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹).

[124] Calculated from h = H₀ / (100 km⋅s⁻¹⋅Mpc⁻¹) per ρ_crit = 1.87847×10⁻²⁶ h²⋅kg⋅m⁻³.^[15]

[DeruelleUzan-1] [1]
Deruelle, Nathalie; Uzan, Jean-Philippe (2018-08-30). de Forcrand-Millard, Patricia (ed.). Relativity in Modern Physics (1 ed.). Oxford University Press. doi:10.1093/oso/9780198786399.001.0001. ISBN 978-0-19-878639-9.

[2] [2]
Maeder, Andre (2017). "An Alternative to the ΛCDM Model: The Case of Scale Invariance". The Astrophysical Journal. 834 (2): 194. arXiv:1701.03964. Bibcode:2017ApJ...834..194M. doi:10.3847/1538-4357/834/2/194. ISSN 0004-637X. S2CID 119513478.

[3] [3]
Brouwer, Margot (2017). "First test of Verlinde's theory of emergent gravity using weak gravitational lensing measurements". Monthly Notices of the Royal Astronomical Society. 466 (3): 2547–2559. arXiv:1612.03034. Bibcode:2017MNRAS.466.2547B. doi:10.1093/mnras/stw3192. S2CID 18916375.

[4] [4]
P. Kroupa, B. Famaey, K.S. de Boer, J. Dabringhausen, M. Pawlowski, C.M. Boily, H. Jerjen, D. Forbes, G. Hensler, M. Metz, "Local-Group tests of dark-matter concordance cosmology. Towards a new paradigm for structure formation" A&A 523, 32 (2010).

[5] [5]
Petit, J. P.; D'Agostini, G. (2018-07-01). "Constraints on Janus Cosmological model from recent observations of supernovae type Ia". Astrophysics and Space Science. 363 (7): 139. Bibcode:2018Ap&SS.363..139D. doi:10.1007/s10509-018-3365-3. ISSN 1572-946X. S2CID 125167116.

[6] [6]
Pandey, Kanhaiya L.; Karwal, Tanvi; Das, Subinoy (2019-10-21). "Alleviating the H0 and S8 Anomalies With a Decaying Dark Matter Model". Journal of Cosmology and Astroparticle Physics. arXiv:1902.10636. doi:10.1088/1475-7516/2020/07/026. S2CID 119234939.

[DavisLineweaver-7] [7]
Davis, Tamara M.; Lineweaver, Charles H. (2004). "Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe". Publications of the Astronomical Society of Australia. 21 (1): 97–109. arXiv:astro-ph/0310808. Bibcode:2004PASA...21...97D. doi:10.1071/AS03040. ISSN 1323-3580.

[8] [8]
DES Collaboration (2018). "First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters". The Astrophysical Journal. 872 (2): L30. arXiv:1811.02374. Bibcode:2019ApJ...872L..30A. doi:10.3847/2041-8213/ab04fa. S2CID 84833144.

[9] [9]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641: A6. arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.

[10] [10]
Persic, M.; et al. (1996). "The universal rotation curve of spiral galaxies — I. The dark matter connection". Monthly Notices of the Royal Astronomical Society. 281 (1): 27–47. arXiv:astro-ph/9506004. Bibcode:1996MNRAS.281...27P. doi:10.1093/mnras/278.1.27.

[11] [11]
Bertone, Gianfranco; Hooper, Dan (2018-10-15). "History of dark matter". Reviews of Modern Physics. 90 (4): 045002. arXiv:1605.04909. Bibcode:2018RvMP...90d5002B. doi:10.1103/RevModPhys.90.045002. ISSN 0034-6861.

[PDG2019-12] [12]
Tanabashi, M.; et al. (Particle Data Group) (2019). "Astrophysical Constants and Parameters" (PDF). Physical Review D. 98 (3). Particle Data Group: 030001. Bibcode:2018PhRvD..98c0001T. doi:10.1103/PhysRevD.98.030001. Retrieved 2020-03-08.

[13] [13]
Persic, Massimo; Salucci, Paolo (1992-09-01). "The baryon content of the Universe". Monthly Notices of the Royal Astronomical Society. 258 (1): 14P–18P. arXiv:astro-ph/0502178. Bibcode:1992MNRAS.258P..14P. doi:10.1093/mnras/258.1.14P. ISSN 0035-8711. S2CID 17945298.

[Dodelson-14] [14]
Dodelson, Scott (2008). Modern cosmology (4 ed.). San Diego, CA: Academic Press. ISBN 978-0-12-219141-1.

[constants-15] [15]
K.A. Olive; et al. (Particle Data Group) (2015). "The Review of Particle Physics. 2. Astrophysical constants and parameters" (PDF). Particle Data Group: Berkeley Lab. Archived from the original (PDF) on 3 December 2015. Retrieved 10 January 2016.

[16] [16]
Frieman, Joshua A.; Turner, Michael S.; Huterer, Dragan (2008). "Dark Energy and the Accelerating Universe". Annual Review of Astronomy and Astrophysics. 46 (1): 385–432. arXiv:0803.0982. Bibcode:2008ARA&A..46..385F. doi:10.1146/annurev.astro.46.060407.145243. S2CID 15117520.

[Snowmass21-17] [17]
Elcio Abdalla; Guillermo Franco Abellán; et al. (11 Mar 2022). "Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies". Journal of High Energy Astrophysics. 34: 49. arXiv:2203.06142v1. Bibcode:2022JHEAp..34...49A. doi:10.1016/j.jheap.2022.04.002. S2CID 247411131.

[cern-courier-18] [18]
Matthew Chalmers (2 July 2021). "Exploring the Hubble tension". CERN Courier. Retrieved 25 March 2022.

[19] [19]
Kovac, J. M.; Leitch, E. M.; Pryke, C.; Carlstrom, J. E.; Halverson, N. W.; Holzapfel, W. L. (2002). "Detection of polarization in the cosmic microwave background using DASI". Nature. 420 (6917): 772–787. arXiv:astro-ph/0209478. Bibcode:2002Natur.420..772K. doi:10.1038/nature01269. PMID 12490941. S2CID 4359884.

[20] [20]
Planck Collaboration (2016). "Planck 2015 Results. XIII. Cosmological Parameters". Astronomy & Astrophysics. 594 (13): A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.

[Turner-21] [21]
Michael Turner (12 Jan 2022). "The Road to Precision Cosmology". Annual Review of Nuclear and Particle Science. 32: 1–35. arXiv:2201.04741. Bibcode:2022ARNPS..72....1T. doi:10.1146/annurev-nucl-111119-041046. S2CID 245906450.

[22] [22]
Andrew Liddle. An Introduction to Modern Cosmology (2nd ed.). London: Wiley, 2003.

[23] [23]
Steven Weinberg (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons, Inc. ISBN 978-0-471-92567-5.

[Colin_et_al-24] [24]
Jacques Colin; Roya Mohayaee; Mohamed Rameez; Subir Sarkar (20 November 2019). "Evidence for anisotropy of cosmic acceleration". Astronomy and Astrophysics. 631: L13. arXiv:1808.04597. Bibcode:2019A&A...631L..13C. doi:10.1051/0004-6361/201936373. S2CID 208175643. Retrieved 25 March 2022.

[FLRW_breakdown-25] [25]
Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble Tension Signal a Breakdown in FLRW Cosmology?". Classical and Quantum Gravity. 38 (18): 184001. arXiv:2105.09790. Bibcode:2021CQGra..38r4001K. doi:10.1088/1361-6382/ac1a81. ISSN 0264-9381. S2CID 234790314.

[Heinesen-MacPherson-26] [26]
Asta Heinesen; Hayley J. Macpherson (15 July 2021). "Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study". Physical Review D. 104 (2): 023525. arXiv:2103.11918. Bibcode:2021PhRvD.104b3525M. doi:10.1103/PhysRevD.104.023525. S2CID 232307363. Retrieved 25 March 2022.

[Ellis_2009-27] [27]
Ellis, G. F. R. (2009). "Dark energy and inhomogeneity". Journal of Physics: Conference Series. 189 (1): 012011. Bibcode:2009JPhCS.189a2011E. doi:10.1088/1742-6596/189/1/012011. S2CID 250670331.

[28] [28]
Lee Billings (April 15, 2020). "Do We Live in a Lopsided Universe?". Scientific American. Retrieved March 24, 2022.

[29] [29]
Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (8 April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX-T scaling relation". Astronomy & Astrophysics. 636 (April 2020): 42. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. S2CID 215238834. Retrieved 24 March 2022.

[30] [30]
Nathan J. Secrest; Sebastian von Hausegger; Mohamed Rameez; Roya Mohayaee; Subir Sarkar; Jacques Colin (February 25, 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal Letters. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. S2CID 222066749.

[31] [31]
B. Javanmardi; C. Porciani; P. Kroupa; J. Pflamm-Altenburg (August 27, 2015). "Probing the Isotropy of Cosmic Acceleration Traced By Type Ia Supernovae". The Astrophysical Journal Letters. 810 (1): 47. arXiv:1507.07560. Bibcode:2015ApJ...810...47J. doi:10.1088/0004-637X/810/1/47. S2CID 54958680. Retrieved March 24, 2022.

[Planck-32] [32]
"Simple but challenging: the Universe according to Planck". ESA Science & Technology. October 5, 2016 [March 21, 2013]. Retrieved October 29, 2016.

[sciama-33] [33]
Dennis Sciama (12 June 1967). "Peculiar Velocity of the Sun and the Cosmic Microwave Background". Physical Review Letters. 18 (24): 1065–1067. Bibcode:1967PhRvL..18.1065S. doi:10.1103/PhysRevLett.18.1065. Retrieved 25 March 2022.

[34] [34]
G. F. R. Ellis; J. E. Baldwin (1 January 1984). "On the expected anisotropy of radio source counts". Monthly Notices of the Royal Astronomical Society. 206 (2): 377–381. doi:10.1093/mnras/206.2.377. Retrieved 25 March 2022.

[35] [35]
Siewert, Thilo M.; Schmidt-Rubart, Matthias; Schwarz, Dominik J. (2021). "Cosmic radio dipole: Estimators and frequency dependence". Astronomy & Astrophysics. 653: A9. arXiv:2010.08366. Bibcode:2021A&A...653A...9S. doi:10.1051/0004-6361/202039840. S2CID 223953708.

[36] [36]
Secrest, Nathan; von Hausegger, Sebastian; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (25 February 2021). "A Test of the Cosmological Principle with Quasars". The Astrophysical Journal. 908 (2): L51. arXiv:2009.14826. Bibcode:2021ApJ...908L..51S. doi:10.3847/2041-8213/abdd40. ISSN 2041-8213. S2CID 222066749.

[37] [37]
Singal, Ashok K. (2022). "Peculiar motion of Solar system from the Hubble diagram of supernovae Ia and its implications for cosmology". Monthly Notices of the Royal Astronomical Society. 515 (4): 5969–5980. arXiv:2106.11968. doi:10.1093/mnras/stac1986.

[38] [38]
Singal, Ashok K. (2022). "Solar system peculiar motion from the Hubble diagram of quasars and testing the cosmological principle". Monthly Notices of the Royal Astronomical Society. 511 (2): 1819–1829. arXiv:2107.09390. doi:10.1093/mnras/stac144.

[39] [39]
de Oliveira-Costa, Angelica; Tegmark, Max; Zaldarriaga, Matias; Hamilton, Andrew (25 March 2004). "The significance of the largest scale CMB fluctuations in WMAP". Physical Review D. 69 (6): 063516. arXiv:astro-ph/0307282. Bibcode:2004PhRvD..69f3516D. doi:10.1103/PhysRevD.69.063516. ISSN 1550-7998. S2CID 119463060.

[40] [40]
Land, Kate; Magueijo, Joao (28 November 2005). "Is the Universe odd?". Physical Review D. 72 (10): 101302. arXiv:astro-ph/0507289. Bibcode:2005PhRvD..72j1302L. doi:10.1103/PhysRevD.72.101302. ISSN 1550-7998. S2CID 119333704.

[41] [41]
Kim, Jaiseung; Naselsky, Pavel (10 May 2010). "Anomalous parity asymmetry of the Wilkinson Microwave Anisotropy Probe power spectrum data at low multipoles". The Astrophysical Journal. 714 (2): L265–L267. arXiv:1001.4613. Bibcode:2010ApJ...714L.265K. doi:10.1088/2041-8205/714/2/L265. ISSN 2041-8205. S2CID 24389919.

[42] [42]
Hutsemekers, D.; Cabanac, R.; Lamy, H.; Sluse, D. (October 2005). "Mapping extreme-scale alignments of quasar polarization vectors". Astronomy & Astrophysics. 441 (3): 915–930. arXiv:astro-ph/0507274. Bibcode:2005A&A...441..915H. doi:10.1051/0004-6361:20053337. ISSN 0004-6361. S2CID 14626666.

[43] [43]
Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the $L_{\text{X}}-T$ scaling relation". Astronomy & Astrophysics. 636: A15. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. ISSN 0004-6361. S2CID 215238834.

[44] [44]
Migkas, K.; Pacaud, F.; Schellenberger, G.; Erler, J.; Nguyen-Dang, N. T.; Reiprich, T. H.; Ramos-Ceja, M. E.; Lovisari, L. (May 2021). "Cosmological implications of the anisotropy of ten galaxy cluster scaling relations". Astronomy & Astrophysics. 649: A151. arXiv:2103.13904. Bibcode:2021A&A...649A.151M. doi:10.1051/0004-6361/202140296. ISSN 0004-6361. S2CID 232352604.

[45] [45]
Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (2022). "Hints of FLRW breakdown from supernovae". Physical Review D. 105 (6): 063514. arXiv:2106.02532. Bibcode:2022PhRvD.105f3514K. doi:10.1103/PhysRevD.105.063514. S2CID 235352881.

[46] [46]
Luongo, Orlando; Muccino, Marco; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (2022). "Larger H0 values in the CMB dipole direction". Physical Review D. 105 (10): 103510. arXiv:2108.13228. Bibcode:2022PhRvD.105j3510L. doi:10.1103/PhysRevD.105.103510. S2CID 248713777.

[Saadeh-47] [47]
Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen, JD (2016). "How Isotropic is the Universe?". Physical Review Letters. 117 (13): 131302. arXiv:1605.07178. Bibcode:2016PhRvL.117m1302S. doi:10.1103/PhysRevLett.117.131302. PMID 27715088. S2CID 453412.

[Yadav-48] [48]
Yadav, Jaswant; J. S. Bagla; Nishikanta Khandai (25 February 2010). "Fractal dimension as a measure of the scale of homogeneity". Monthly Notices of the Royal Astronomical Society. 405 (3): 2009–2015. arXiv:1001.0617. Bibcode:2010MNRAS.405.2009Y. doi:10.1111/j.1365-2966.2010.16612.x. S2CID 118603499.

[apj624_2_463-49] [49]
Gott, J. Richard III; et al. (May 2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484. arXiv:astro-ph/0310571. Bibcode:2005ApJ...624..463G. doi:10.1086/428890. S2CID 9654355.

[50] [50]
Horvath, I.; Hakkila, J.; Bagoly, Z. (2013). "The largest structure of the Universe, defined by Gamma-Ray Bursts". arXiv:1311.1104 [astro-ph.CO].

[51] [51]
"Line of galaxies is so big it breaks our understanding of the universe".

[52] [52]
Cooper, Keith (22 January 2024). "An impossibly huge ring of galaxies might lead us to new physics. Here's how". Space.com. Retrieved 31 January 2024.

[Nadathur-53] [53]
Nadathur, Seshadri (2013). "Seeing patterns in noise: gigaparsec-scale 'structures' that do not violate homogeneity". Monthly Notices of the Royal Astronomical Society. 434 (1): 398–406. arXiv:1306.1700. Bibcode:2013MNRAS.434..398N. doi:10.1093/mnras/stt1028. S2CID 119220579.

[Asencio-54] [54]
Asencio, E; Banik, I; Kroupa, P (2021-02-21). "A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology". Monthly Notices of the Royal Astronomical Society. 500 (2): 5249–5267. arXiv:2012.03950. Bibcode:2021MNRAS.500.5249A. doi:10.1093/mnras/staa3441. ISSN 0035-8711.

[Asencio_2023-55] [55]
Asencio, E; Banik, I; Kroupa, P (2023-09-10). "A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology". The Astrophysical Journal. 954 (2): 162. arXiv:2308.00744. Bibcode:2023ApJ...954..162A. doi:10.3847/1538-4357/ace62a. ISSN 1538-4357.

[Katz-56] [56]
Katz, H; McGaugh, S; Teuben, P; Angus, G. W. (2013-07-20). "Galaxy Cluster Bulk Flows and Collision Velocities in QUMOND". The Astrophysical Journal. 772 (1): 10. arXiv:1305.3651. Bibcode:2013ApJ...772...10K. doi:10.1088/0004-637X/772/1/10. ISSN 1538-4357.

[kbc-57] [57]
Keenan, Ryan C.; Barger, Amy J.; Cowie, Lennox L. (2013). "Evidence for a ~300 Mpc Scale Under-density in the Local Galaxy Distribution". The Astrophysical Journal. 775 (1): 62. arXiv:1304.2884. Bibcode:2013ApJ...775...62K. doi:10.1088/0004-637X/775/1/62. S2CID 118433293.

[siegel-58] [58]
Siegel, Ethan. "We're Way Below Average! Astronomers Say Milky Way Resides In A Great Cosmic Void". Forbes. Retrieved 2017-06-09.

[Haslbauer-59] [59]
Haslbauer, M; Banik, I; Kroupa, P (2020-12-21). "The KBC void and Hubble tension contradict LCDM on a Gpc scale – Milgromian dynamics as a possible solution". Monthly Notices of the Royal Astronomical Society. 499 (2): 2845–2883. arXiv:2009.11292. Bibcode:2020MNRAS.499.2845H. doi:10.1093/mnras/staa2348. ISSN 0035-8711.

[60] [60]
Sahlén, Martin; Zubeldía, Íñigo; Silk, Joseph (2016). "Cluster–Void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void". The Astrophysical Journal Letters. 820 (1): L7. arXiv:1511.04075. Bibcode:2016ApJ...820L...7S. doi:10.3847/2041-8205/820/1/L7. ISSN 2041-8205. S2CID 119286482.

[di_Valentino_2021_153001-61] [61]
di Valentino, Eleonora; Mena, Olga; Pan, Supriya; et al. (2021). "In the realm of the Hubble tension—a review of solutions". Classical and Quantum Gravity. 38 (15): 153001. arXiv:2103.01183. Bibcode:2021CQGra..38o3001D. doi:10.1088/1361-6382/ac086d. S2CID 232092525.

[LS-20190826-62] [62]
Mann, Adam (26 August 2019). "One Number Shows Something Is Fundamentally Wrong with Our Conception of the Universe – This fight has universal implications". Live Science. Retrieved 26 August 2019.

[63] [63]
Gresko, Michael (17 December 2021). "The universe is expanding faster than it should be". nationalgeographic.com. National Geographic. Archived from the original on December 17, 2021. Retrieved 21 December 2021.

[64] [64]
Shanks, T; Hogarth, L M; Metcalfe, N (2019-03-21). "Gaia Cepheid parallaxes and 'Local Hole' relieve H 0 tension". Monthly Notices of the Royal Astronomical Society: Letters. 484 (1): L64–L68. arXiv:1810.02595. Bibcode:2019MNRAS.484L..64S. doi:10.1093/mnrasl/sly239. ISSN 1745-3925.

[65] [65]
Kenworthy, W. D'Arcy; Scolnic, Dan; Riess, Adam (2019-04-24). "The Local Perspective on the Hubble Tension: Local Structure Does Not Impact Measurement of the Hubble Constant". The Astrophysical Journal. 875 (2): 145. arXiv:1901.08681. Bibcode:2019ApJ...875..145K. doi:10.3847/1538-4357/ab0ebf. ISSN 1538-4357. S2CID 119095484.

[66] [66]
Poulin, Vivian; Smith, Tristan L.; Karwal, Tanvi; Kamionkowski, Marc (2019-06-04). "Early Dark Energy can Resolve the Hubble Tension". Physical Review Letters. 122 (22): 221301. arXiv:1811.04083. Bibcode:2019PhRvL.122v1301P. doi:10.1103/PhysRevLett.122.221301. PMID 31283280. S2CID 119233243.

[67] [67]
Planck Collaboration; Aghanim, N.; Akrami, Y.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B.; Bartolo, N.; Basak, S.; Battye, R.; Benabed, K.; Bernard, J.-P.; Bersanelli, M. (September 2020). "Planck 2018 results: VI. Cosmological parameters (Corrigendum)". Astronomy & Astrophysics. 652: C4. doi:10.1051/0004-6361/201833910e. hdl:10902/24951. ISSN 0004-6361.

[68] [68]
Heymans, Catherine; Tröster, Tilman; Asgari, Marika; Blake, Chris; Hildebrandt, Hendrik; Joachimi, Benjamin; Kuijken, Konrad; Lin, Chieh-An; Sánchez, Ariel G.; van den Busch, Jan Luca; Wright, Angus H.; Amon, Alexandra; Bilicki, Maciej; de Jong, Jelte; Crocce, Martin (February 2021). "KiDS-1000 Cosmology: Multi-probe weak gravitational lensing and spectroscopic galaxy clustering constraints". Astronomy & Astrophysics. 646: A140. arXiv:2007.15632. Bibcode:2021A&A...646A.140H. doi:10.1051/0004-6361/202039063. ISSN 0004-6361.

[69] [69]
Wood, Charlie (8 September 2020). "A New Cosmic Tension: The Universe Might Be Too Thin". Quanta Magazine.

[70] [70]
Abbott, T. M. C.; Aguena, M.; Alarcon, A.; Allam, S.; Alves, O.; Amon, A.; Andrade-Oliveira, F.; Annis, J.; Avila, S.; Bacon, D.; Baxter, E.; Bechtol, K.; Becker, M. R.; Bernstein, G. M.; Bhargava, S. (2022-01-13). "Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing". Physical Review D. 105 (2): 023520. arXiv:2105.13549. Bibcode:2022PhRvD.105b3520A. doi:10.1103/PhysRevD.105.023520. hdl:11368/3013060. ISSN 2470-0010.

[71] [71]
Dark Energy Survey; Kilo-Degree Survey Collaboration; Abbott, T.M.C.; Aguena, M.; Alarcon, A.; Alves, O.; Amon, A.; Andrade-Oliveira, F.; Asgari, M.; Avila, S.; Bacon, D.; Bechtol, K.; Becker, M. R.; Bernstein, G. M.; Bertin, E. (2023-10-20). "DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys". The Open Journal of Astrophysics. 6: 36. arXiv:2305.17173. Bibcode:2023OJAp....6E..36D. doi:10.21105/astro.2305.17173. ISSN 2565-6120.

[72] [72]
Li, Xiangchong; Zhang, Tianqing; Sugiyama, Sunao; Dalal, Roohi; Terasawa, Ryo; Rau, Markus M.; Mandelbaum, Rachel; Takada, Masahiro; More, Surhud; Strauss, Michael A.; Miyatake, Hironao; Shirasaki, Masato; Hamana, Takashi; Oguri, Masamune; Luo, Wentao (2023-12-11). "Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear two-point correlation functions". Physical Review D. 108 (12): 123518. arXiv:2304.00702. Bibcode:2023PhRvD.108l3518L. doi:10.1103/PhysRevD.108.123518. ISSN 2470-0010.

[73] [73]
Dalal, Roohi; Li, Xiangchong; Nicola, Andrina; Zuntz, Joe; Strauss, Michael A.; Sugiyama, Sunao; Zhang, Tianqing; Rau, Markus M.; Mandelbaum, Rachel; Takada, Masahiro; More, Surhud; Miyatake, Hironao; Kannawadi, Arun; Shirasaki, Masato; Taniguchi, Takanori (2023-12-11). "Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra". Physical Review D. 108 (12): 123519. arXiv:2304.00701. Bibcode:2023PhRvD.108l3519D. doi:10.1103/PhysRevD.108.123519. ISSN 2470-0010.

[74] [74]
Yoon, Mijin (2023-12-11). "Inconsistency Turns Up Again for Cosmological Observations". Physics. 16 (12): 193. arXiv:2304.00701. Bibcode:2023PhRvD.108l3519D. doi:10.1103/PhysRevD.108.123519.

[75] [75]
Kruesi, Liz (19 January 2024). "Clashing Cosmic Numbers Challenge Our Best Theory of the Universe". Quanta Magazine.

[76] [76]
Ghirardini, V.; Bulbul, E.; Artis, E.; Clerc, N.; Garrel, C.; Grandis, S.; Kluge, M.; Liu, A.; Bahar, Y. E.; Balzer, F.; Chiu, I.; Comparat, J.; Gruen, D.; Kleinebreil, F.; Krippendorf, S. (February 2024). "The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic Hemisphere". arXiv:2402.08458 [astro-ph.CO].

[77] [77]
Kruesi, Liz (4 March 2024). "Fresh X-Rays Reveal a Universe as Clumpy as Cosmology Predicts". Quanta Magazine.

[78] [78]
Said, Khaled; Colless, Matthew; Magoulas, Christina; Lucey, John R; Hudson, Michael J (2020-09-01). "Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity". Monthly Notices of the Royal Astronomical Society. 497 (1): 1275–1293. arXiv:2007.04993. doi:10.1093/mnras/staa2032. ISSN 0035-8711.

[79] [79]
Boruah, Supranta S; Hudson, Michael J; Lavaux, Guilhem (2020-09-21). "Cosmic flows in the nearby Universe: new peculiar velocities from SNe and cosmological constraints". Monthly Notices of the Royal Astronomical Society. 498 (2): 2703–2718. arXiv:1912.09383. doi:10.1093/mnras/staa2485. ISSN 0035-8711.

[LandMagueijo2005-80] [80]

[Saadeh2016-81] [81]

[fields11-82] [82]
Fields, B. D. (2011). "The primordial lithium problem". Annual Review of Nuclear and Particle Science. 61 (1): 47–68. arXiv:1203.3551. Bibcode:2011ARNPS..61...47F. doi:10.1146/annurev-nucl-102010-130445.

[83] [83]
Eleonora Di Valentino; Alessandro Melchiorri; Joseph Silk (4 November 2019). "Planck evidence for a closed Universe and a possible crisis for cosmology". Nature Astronomy. 4 (2): 196–203. arXiv:1911.02087. doi:10.1038/s41550-019-0906-9. S2CID 207880880. Retrieved 24 March 2022.

[84] [84]
Philip Bull; Marc Kamionkowski (15 April 2013). "What if Planck's Universe isn't flat?". Physical Review D. 87 (3): 081301. arXiv:1302.1617. Bibcode:2013PhRvD..87h1301B. doi:10.1103/PhysRevD.87.081301. S2CID 118437535. Retrieved 24 March 2022.

[85] [85]
Chae, Kyu-Hyun; Lelli, Federico; Desmond, Harry; McGaugh, Stacy S.; Li, Pengfei; Schombert, James M. (2020). "Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies". The Astrophysical Journal. 904 (1): 51. arXiv:2009.11525. Bibcode:2020ApJ...904...51C. doi:10.3847/1538-4357/abbb96. S2CID 221879077.

[86] [86]
Paranjape, Aseem; Sheth, Ravi K (2022-10-04). "The phenomenology of the external field effect in cold dark matter models". Monthly Notices of the Royal Astronomical Society. 517 (1): 130–139. arXiv:2112.00026. doi:10.1093/mnras/stac2689. ISSN 0035-8711.

[87] [87]
Freundlich, Jonathan; Famaey, Benoit; Oria, Pierre-Antoine; Bílek, Michal; Müller, Oliver; Ibata, Rodrigo (2022-02-01). "Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies". Astronomy & Astrophysics. 658: A26. arXiv:2109.04487. Bibcode:2022A&A...658A..26F. doi:10.1051/0004-6361/202142060. ISSN 0004-6361. We hence do not see any evidence for a violation of the strong equivalence principle in Coma cluster UDGs, contrarily to, for instance, Chae et al. (2020, 2021), for disc galaxies in the field. Our work extends that of Bílek et al. (2019b) and Haghi et al. (2019a), which is limited to DF44 and makes the result all the more compelling. We recall that the MOND predictions do not involve any free parameter.

[88] [88]
Kroupa, P.; Famaey, B.; de Boer, Klaas S.; Dabringhausen, Joerg; Pawlowski, Marcel; Boily, Christian; Jerjen, Helmut; Forbes, Duncan; Hensler, Gerhard (2010). "Local-Group tests of dark-matter Concordance Cosmology: Towards a new paradigm for structure formation". Astronomy and Astrophysics. 523: 32–54. arXiv:1006.1647. Bibcode:2010A&A...523A..32K. doi:10.1051/0004-6361/201014892. S2CID 11711780.

[89] [89]
Gentile, G.; Salucci, P. (2004). "The cored distribution of dark matter in spiral galaxies". Monthly Notices of the Royal Astronomical Society. 351 (3): 903–922. arXiv:astro-ph/0403154. Bibcode:2004MNRAS.351..903G. doi:10.1111/j.1365-2966.2004.07836.x. S2CID 14308775.

[Klypin-90] [90]
Klypin, Anatoly; Kravtsov, Andrey V.; Valenzuela, Octavio; Prada, Francisco (1999). "Where are the missing galactic satellites?". Astrophysical Journal. 522 (1): 82–92. arXiv:astro-ph/9901240. Bibcode:1999ApJ...522...82K. doi:10.1086/307643. S2CID 12983798.

[Pawlowski-91] [91]
Pawlowski, Marcel; et al. (2014). "Co-orbiting satellite galaxy structures are still in conflict with the distribution of primordial dwarf galaxies". Monthly Notices of the Royal Astronomical Society. 442 (3): 2362–2380. arXiv:1406.1799. Bibcode:2014MNRAS.442.2362P. doi:10.1093/mnras/stu1005.

[Sawala-92] [92]
Sawala, Till; Cautun, Marius; Frenk, Carlos; et al. (2022). "The Milky Way's plane of satellites: consistent with ΛCDM". Nature Astronomy. 7 (4): 481–491. arXiv:2205.02860. Bibcode:2023NatAs...7..481S. doi:10.1038/s41550-022-01856-z. S2CID 254920916.

[93] [93]
Banik, Indranil; Zhao, H (2018-01-21). "A plane of high velocity galaxies across the Local Group". Monthly Notices of the Royal Astronomical Society. 473 (3): 4033–4054. arXiv:1701.06559. Bibcode:2018MNRAS.473.4033B. doi:10.1093/mnras/stx2596. ISSN 0035-8711.

[94] [94]
Banik, Indranil; Haslbauer, Moritz; Pawlowski, Marcel S.; Famaey, Benoit; Kroupa, Pavel (2021-06-21). "On the absence of backsplash analogues to NGC 3109 in the ΛCDM framework". Monthly Notices of the Royal Astronomical Society. 503 (4): 6170–6186. arXiv:2105.04575. Bibcode:2021MNRAS.503.6170B. doi:10.1093/mnras/stab751. ISSN 0035-8711.

[kormendy2010-95] [95]
Kormendy, J.; Drory, N.; Bender, R.; Cornell, M.E. (2010). "Bulgeless giant galaxies challenge our picture of galaxy formation by hierarchical clustering". The Astrophysical Journal. 723 (1): 54–80. arXiv:1009.3015. Bibcode:2010ApJ...723...54K. doi:10.1088/0004-637X/723/1/54. S2CID 119303368.

[Haslbauer2022-96] [96]
Haslbauer, M; Banik, I; Kroupa, P; Wittenburg, N; Javanmardi, B (2022-02-01). "The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology". The Astrophysical Journal. 925 (2): 183. arXiv:2202.01221. Bibcode:2022ApJ...925..183H. doi:10.3847/1538-4357/ac46ac. ISSN 1538-4357.

[sachdeva2016-97] [97]
Sachdeva, S.; Saha, K. (2016). "Survival of pure disk galaxies over the last 8 billion years". The Astrophysical Journal Letters. 820 (1): L4. arXiv:1602.08942. Bibcode:2016ApJ...820L...4S. doi:10.3847/2041-8205/820/1/L4. S2CID 14644377.

[Roshan2021-98] [98]
Mahmood, R; Ghafourian, N; Kashfi, T; Banik, I; Haslbauer, M; Cuomo, V; Famaey, B; Kroupa, P (2021-11-01). "Fast galaxy bars continue to challenge standard cosmology". Monthly Notices of the Royal Astronomical Society. 508 (1): 926–939. arXiv:2106.10304. Bibcode:2021MNRAS.508..926R. doi:10.1093/mnras/stab2553. hdl:10023/24680. ISSN 0035-8711.

[99] [99]
Rini, Matteo (2017). "Synopsis: Tackling the Small-Scale Crisis". Physical Review D. 95 (12): 121302. arXiv:1703.10559. Bibcode:2017PhRvD..95l1302N. doi:10.1103/PhysRevD.95.121302. S2CID 54675159.

[NASA-milestone-100] [100]
Cesari, Thaddeus (9 December 2022). "NASA's Webb Reaches New Milestone in Quest for Distant Galaxies". Retrieved 9 December 2022.

[Curtis-Lake2022-101] [101]
Curtis-Lake, Emma; et al. (December 2022). "Spectroscopy of four metal-poor galaxies beyond redshift ten" (PDF). arXiv:2212.04568.

[SmithEtAl-2022-102] [102]
Smith, Tristian L.; Lucca, Matteo; Poulin, Vivian; Abellan, Guillermo F.; Balkenhol, Lennart; Benabed, Karim; Galli, Silvia; Murgia, Riccardo (August 2022). "Hints of early dark energy in Planck, SPT, and ACT data: New physics or systematics?". Physical Review D. 106 (4): 043526. arXiv:2202.09379. Bibcode:2022PhRvD.106d3526S. doi:10.1103/PhysRevD.106.043526. S2CID 247011465.

[Boylan-Kolchin-103] [103]
Boylan-Kolchin, Michael (2023). "Stress testing ΛCDM with high-redshift galaxy candidates". Nature Astronomy. 7 (6): 731–735. arXiv:2208.01611. Bibcode:2023NatAs...7..731B. doi:10.1038/s41550-023-01937-7. PMC 10281863. PMID 37351007. S2CID 251252960.

[SciAm2022-104] [104]
O'Callaghan, Jonathan (6 December 2022). "Astronomers Grapple with JWST's Discovery of Early Galaxies". Scientific American. Retrieved 10 December 2022.

[BehrooziEtAl-105] [105]
Behroozi, Peter; Conroy, Charlie; Wechsler, Risa H.; Hearin, Andrew; Williams, Christina C.; Moster, Benjamin P.; Yung, L. Y. Aaron; Somerville, Rachel S.; Gottlöber, Stefan; Yepes, Gustavo; Endsley, Ryan (December 2020). "The Universe at z > 10: predictions for JWST from the UNIVERSEMACHINE DR1". Monthly Notices of the Royal Astronomical Society. 499 (4): 5702–5718. arXiv:2007.04988. Bibcode:2020MNRAS.499.5702B. doi:10.1093/mnras/staa3164.

[SpringelHernquist-106] [106]
Volker Springel; Lars Hernquist (February 2003). "The history of star formation in a Λ cold dark matter universe". Monthly Notices of the Royal Astronomical Society. 339 (2): 312–334. arXiv:astro-ph/0206395. Bibcode:2003MNRAS.339..312S. doi:10.1046/j.1365-8711.2003.06207.x. S2CID 8715136.

[107] [107]
Persic, M.; Salucci, P. (1992-09-01). "The baryon content of the Universe". Monthly Notices of the Royal Astronomical Society. 258 (1): 14P–18P. arXiv:astro-ph/0502178. Bibcode:1992MNRAS.258P..14P. doi:10.1093/mnras/258.1.14P. ISSN 0035-8711.

[108] [108]
Chaves-Montero, Jonás; Hernández-Monteagudo, Carlos; Angulo, Raúl E; Emberson, J D (2021-03-25). "Measuring the evolution of intergalactic gas from z = 0 to 5 using the kinematic Sunyaev–Zel'dovich effect". Monthly Notices of the Royal Astronomical Society. 503 (2): 1798–1814. arXiv:1911.10690. doi:10.1093/mnras/staa3782. ISSN 0035-8711.

[109] [109]
Merritt, David (2017). "Cosmology and convention". Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 57: 41–52. arXiv:1703.02389. Bibcode:2017SHPMP..57...41M. doi:10.1016/j.shpsb.2016.12.002. S2CID 119401938.

[Planck_2015-110] [110]
Planck Collaboration (2016). "Planck 2015 results. XIII. Cosmological parameters". Astronomy & Astrophysics. 594 (13): A13. arXiv:1502.01589. Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.

[111] [111]
Planck 2015,^[110] p. 32, table 4, last column.

[112] [112]
Planck 2015,^[110] p. 32, table 4, last column.

[Planck_2018-113] [113]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column). arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.

[114] [114]
Appendix A of the LSST Science Book Version 2.0 Archived 2013-02-26 at the Wayback Machine

[115] [115]
p. 7 of Findings of the Joint Dark Energy Mission Figure of Merit Science Working Group

[Planck_2018age-117] [116]
Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column). arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.

[oldwmap-118] [117]
Table 8 on p. 39 of Jarosik, N. et al. (WMAP Collaboration) (2011). "Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results" (PDF). The Astrophysical Journal Supplement Series. 192 (2): 14. arXiv:1001.4744. Bibcode:2011ApJS..192...14J. doi:10.1088/0067-0049/192/2/14. hdl:2152/43001. S2CID 46171526. Retrieved 2010-12-04. (from NASA's WMAP Documents page)

[125] [118]
Planck Collaboration; Adam, R.; Aghanim, N.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J.; Barreiro, R. B. (2016-05-11). "Planck intermediate results. XLVII. Planck constraints on reionization history". Astronomy & Astrophysics. 596 (108): A108. arXiv:1605.03507. Bibcode:2016A&A...596A.108P. doi:10.1051/0004-6361/201628897. S2CID 5892152.

[126] [119]
Spergel, D. N. (2015). "The dark side of the cosmology: dark matter and dark energy". Science. 347 (6226): 1100–1102. Bibcode:2015Sci...347.1100S. doi:10.1126/science.aaa0980. PMID 25745164.

[127] [120]
Zyla, P.A.; et al. (Particle Data Group) (2020). "Cosmological Parameters" (PDF). Prog. Theor. Exp. Phys. 083C01.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

[48]

[49]

[50]

[51]

[52]

[53]

[54]

[55]

[56]

[57]

[58]

[59]

[60]

[61]

[62]

[63]

[64]

[65]

[66]

[67]

[68]

[69]

[70]

[71]

[72]

[73]

[74]

[75]

[76]

[77]

[78]

[79]

[80]

[81]

[82]

[83]

[84]

[85]

[86]

[87]

[88]

[89]

[90]

[91]

[92]

[93]

[94]

[95]

[96]

[97]

[98]

[99]

[100]

Lambda-CDM model

Lack of detection

Violations of the cosmological principle

Violations of isotropy

Violations of homogeneity

El Gordo galaxy cluster collision

KBC void

Hubble tension

S₈ tension

Axis of evil

Cosmological lithium problem

Shape of the universe

Violations of the strong equivalence principle

Cold dark matter discrepancies

Cuspy halo problem

Dwarf galaxy problem

Satellite disk problem

High-velocity galaxy problem

Galaxy morphology problem

Fast galaxy bar problem

Small scale crisis

High redshift galaxies

Missing baryon problem

Unfalsifiability

Wikiwand in your browser!

Overview

Cosmic expansion history

Historical development

Successes

Challenges

Parameters

Extended models

See also

References

Further reading

External links

Lack of detection

Violations of the cosmological principle

Violations of isotropy

Violations of homogeneity

El Gordo galaxy cluster collision

KBC void

Hubble tension

S8 tension

Axis of evil

Cosmological lithium problem

Shape of the universe

Violations of the strong equivalence principle

Cold dark matter discrepancies

Cuspy halo problem

Dwarf galaxy problem

Satellite disk problem

High-velocity galaxy problem

Galaxy morphology problem

Fast galaxy bar problem

Small scale crisis

High redshift galaxies

Missing baryon problem

Unfalsifiability

Overview

Cosmic expansion history

Historical development

Successes

Challenges

Parameters

Extended models

See also

References

Further reading

External links

S₈ tension