The epoch of reionization is one of the major phase transitions in the history of the universe, and is a focus of ongoing and upcoming cosmic microwave background (CMB) experiments with improved sensitivity to small-scale fluctuations. Reionization also represents a significant contaminant to CMB-derived cosmological parameter constraints, due to the degeneracy between the Thomson-scattering optical depth, $\tau$, and the amplitude of scalar perturbations, $A_s$. This degeneracy subsequently hinders the ability of large-scale structure data to constrain the sum of the neutrino masses, a major target for cosmology in the 2020s. In this work, we explore the kinematic Sunyaev-Zel'dovich (kSZ) effect as a probe of reionization, and show that it can be used to mitigate the optical depth degeneracy with high-sensitivity, high-resolution data from the upcoming CMB-S4 experiment. We discuss the dependence of the kSZ power spectrum on physical reionization model parameters, as well as on empirical reionization parameters, namely $\tau$ and the duration of reionization, $\Delta z$. We show that by combining the kSZ two-point function and the reconstructed kSZ four-point function, degeneracies between $\tau$ and $\Delta z$ can be strongly broken, yielding tight constraints on both parameters. We forecast $\sigma(\tau) = 0.003$ and $\sigma(\Delta z) = 0.25$ for a combination of CMB-S4 and Planck data, including detailed treatment of foregrounds and atmospheric noise. The constraint on $\tau$ is nearly identical to the cosmic-variance limit that can be achieved from large-angle CMB polarization data. The kSZ effect thus promises to yield not only detailed information about the reionization epoch, but also to enable high-precision cosmological constraints on the neutrino mass.

Despite two decades of tremendous experimental and theoretical progress, the riddle of the accelerated expansion of the Universe remains to be solved. On the experimental side, our understanding of the possibilities and limitations of the major dark energy probes has evolved; here we summarize the major probes and their crucial challenges. On the theoretical side, the taxonomy of explanations for the accelerated expansion rate is better understood, providing clear guidance to the relevant observables. We argue that: i) improving statistical precision and systematic control by taking more data, supporting research efforts to address crucial challenges for each probe, using complementary methods, and relying on cross-correlations is well motivated; ii) blinding of analyses is difficult but ever more important; iii) studies of dark energy and modified gravity are related; and iv) it is crucial that R&D for a vibrant dark energy program in the 2030s be started now by supporting studies and technical R&D that will allow embryonic proposals to mature. Understanding dark energy, arguably the biggest unsolved mystery in both fundamental particle physics and cosmology, will remain one of the focal points of cosmology in the forthcoming decade.

Single-object imaging and spectroscopy on telescopes with apertures ranging from ~4 m to 40 m have the potential to greatly enhance the cosmological constraints that can be obtained from LSST. Two major cosmological probes will benefit greatly from LSST follow-up: accurate spectrophotometry for nearby and distant Type Ia supernovae will expand the cosmological distance lever arm by unlocking the constraining power of high-z supernovae; and cosmology with time delays of strongly-lensed supernovae and quasars will require additional high-cadence imaging to supplement LSST, adaptive optics imaging or spectroscopy for accurate lens and source positions, and IFU or slit spectroscopy to measure detailed properties of lens systems. We highlight the scientific impact of these two science drivers, and discuss how additional resources will benefit them. For both science cases, LSST will deliver a large sample of objects over both the wide and deep fields in the LSST survey, but additional data to characterize both individual systems and overall systematics will be key to ensuring robust cosmological inference to high redshifts. Community access to large amounts of natural-seeing imaging on ~2-4 m telescopes, adaptive optics imaging and spectroscopy on 8-40 m telescopes, and high-throughput single-target spectroscopy on 4-40 m telescopes will be necessary for LSST time domain cosmology to reach its full potential. In two companion white papers we present the additional gains for LSST cosmology that will come from deep and from wide-field multi-object spectroscopy.

Community access to deep (i ~ 25), highly-multiplexed optical and near-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatly improve measurements of cosmological parameters from LSST. The largest gain would come from improvements to LSST photometric redshifts, which are employed directly or indirectly for every major LSST cosmological probe; deep spectroscopic datasets will enable reduced uncertainties in the redshifts of individual objects via optimized training. Such spectroscopy will also determine the relationship of galaxy SEDs to their environments, key observables for studies of galaxy evolution. The resulting data will also constrain the impact of blending on photo-z's. Focused spectroscopic campaigns can also improve weak lensing cosmology by constraining the intrinsic alignments between the orientations of galaxies. Galaxy cluster studies can be enhanced by measuring motions of galaxies in and around clusters and by testing photo-z performance in regions of high density. Photometric redshift and intrinsic alignment studies are best-suited to instruments on large-aperture telescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST) but cluster investigations can be pursued with smaller-field instruments (e.g., Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributed amongst a variety of telescopes. However, community access to large amounts of nights for surveys will still be needed to accomplish this work. In two companion white papers we present gains from shallower, wide-area MOS and from single-target imaging and spectroscopy.

LSST will open new vistas for cosmology in the next decade, but it cannot reach its full potential without data from other telescopes. Cosmological constraints can be greatly enhanced using wide-field ($>20$ deg$^2$ total survey area), highly-multiplexed optical and near-infrared multi-object spectroscopy (MOS) on 4-15m telescopes. This could come in the form of suitably-designed large surveys and/or community access to add new targets to existing projects. First, photometric redshifts can be calibrated with high precision using cross-correlations of photometric samples against spectroscopic samples at $0 < z < 3$ that span thousands of sq. deg. Cross-correlations of faint LSST objects and lensing maps with these spectroscopic samples can also improve weak lensing cosmology by constraining intrinsic alignment systematics, and will also provide new tests of modified gravity theories. Large samples of LSST strong lens systems and supernovae can be studied most efficiently by piggybacking on spectroscopic surveys covering as much of the LSST extragalactic footprint as possible (up to $\sim20,000$ square degrees). Finally, redshifts can be measured efficiently for a high fraction of the supernovae in the LSST Deep Drilling Fields (DDFs) by targeting their hosts with wide-field spectrographs. Targeting distant galaxies, supernovae, and strong lens systems over wide areas in extended surveys with (e.g.) DESI or MSE in the northern portion of the LSST footprint or 4MOST in the south could realize many of these gains; DESI, 4MOST, Subaru/PFS, or MSE would all be well-suited for DDF surveys. The most efficient solution would be a new wide-field, highly-multiplexed spectroscopic instrument in the southern hemisphere with $>6$m aperture. In two companion white papers we present gains from deep, small-area MOS and from single-target imaging and spectroscopy.

The Sunyaev-Zel'dovich (SZ) effect introduces a specific distortion of the blackbody spectrum of the cosmic microwave background (CMB) radiation when it scatters off hot gas in clusters of galaxies. The frequency dependence of the distortion is only independent of the cluster redshift when the evolution of the CMB radiation is adiabatic. Using 370 clusters within the redshift range 0.07 ≲ z ≲ 1.4 from the largest SZ-selected cluster sample to date from the Atacama Cosmology Telescope, we provide new constraints on the deviation of CMB temperature evolution from the standard model α =0.017-0.032+0.029, where T(z)=T0(1+z)1-α. This result is consistent with no deviation from the standard adiabatic model. Combining it with previous, independent data sets we obtain a joint constraint of α = -0.001 ± 0.012. Attributing deviation from adiabaticity to the decay of dark energy, this result constrains its effective equation of state weff=-0.998-0.010+0.008.

We use microwave temperature maps from two seasons of data from the Atacama Cosmology Telescope at 146 GHz, together with the "Constant Mass" CMASS galaxy sample from the Baryon Oscillation Spectroscopic Survey to measure the kinematic Sunyaev-Zel'dovich (kSZ) effect over the redshift range z=0.4-0.7. We use galaxy positions and the continuity equation to obtain a reconstruction of the line-of-sight velocity field. We stack the microwave temperature at the location of each halo, weighted by the corresponding reconstructed velocity. We vary the size of the aperture photometry filter used, thus probing the free electron profile of these halos from within the virial radius out to three virial radii, on the scales relevant for investigating the missing baryons problem. The resulting best fit kSZ model is preferred over the no-kSZ hypothesis at 3.3 and 2.9σ for two independent velocity reconstruction methods, using 25,537 galaxies over 660 square degrees. The data suggest that the baryon profile is shallower than the dark matter in the inner regions of the halos probed here, potentially due to energy injection from active galactic nucleus or supernovae. Thus, by constraining the gas profile on a wide range of scales, this technique will be useful for understanding the role of feedback in galaxy groups and clusters. The effect of foregrounds that are uncorrelated with the galaxy velocities is expected to be well below our signal, and residual thermal Sunyaev-Zel'dovich contamination is controlled by masking the most massive clusters. Finally, we discuss the systematics involved in converting our measurement of the kSZ amplitude into the mean free electron fraction of the halos in our sample.

We present ΛCDM cosmological parameter constraints obtained from delensed microwave background power spectra. Lensing maps from a subset of DR4 data from the Atacama Cosmology Telescope (ACT) are used to undo the lensing effect in ACT spectra observed at 150 and 98 GHz. At 150 GHz, we remove the lensing distortion with an effective efficiency of 30% (TT), 30% (EE), 26% (TE) and 20% (BB); this results in detections of the delensing effect at 8.7σ (TT), 5.1σ (EE), 2.6σ (TE), and 2.4σ (BB) significance. The combination of 150 and 98 GHz TT, EE, and TE delensed spectra is well fit by a standard ΛCDM model. We also measure the shift in best-fit parameters when fitting delensed versus lensed spectra; while this shift does not inform our ability to measure cosmological parameters, it does provide a three-way consistency check among the lensing inferred from the best-fit parameters, the lensing in the CMB power spectrum, and the reconstructed lensing map. This shift is predicted to be zero when fitting with the correct model since both lensed and delensed spectra originate from the same region of sky. Fitting with a ΛCDM model and marginalizing over foregrounds, we find that the shift in cosmological parameters is consistent with zero. Our results show that gravitational lensing of the microwave background is internally consistent within the framework of the standard cosmological model.

The early dark energy (EDE) scenario aims to increase the value of the Hubble constant (H0) inferred from cosmic microwave background (CMB) data over that found in the standard cosmological model (ΛCDM), via the introduction of a new form of energy density in the early Universe. The EDE component briefly accelerates cosmic expansion just prior to recombination, which reduces the physical size of the sound horizon imprinted in the CMB. Previous work has found that nonzero EDE is not preferred by Planck CMB power spectrum data alone, which yield a 95% confidence level (C.L.) upper limit fEDE<0.087 on the maximal fractional contribution of the EDE field to the cosmic energy budget. In this paper, we fit the EDE model to CMB data from the Atacama Cosmology Telescope (ACT) data release 4. We find that a combination of ACT, large-scale Planck TT (similar to WMAP), Planck CMB lensing, and BAO data prefers the existence of EDE at >99.7% C.L.: fEDE=0.091-0.036+0.020, with H0=70.9-2.0+1.0 km/s/Mpc (both 68% C.L.). From a model-selection standpoint, we find that EDE is favored over ΛCDM by these data at roughly 3σ significance. In contrast, a joint analysis of the full Planck and ACT data yields no evidence for EDE, as previously found for Planck alone. We show that the preference for EDE in ACT alone is driven by its TE and EE power spectrum data. The tight constraint on EDE from Planck alone is driven by its high-ℓ TT power spectrum data. Understanding whether these differing constraints are physical in nature, due to systematics, or simply a rare statistical fluctuation is of high priority. The best-fit EDE models to ACT and Planck exhibit coherent differences across a wide range of multipoles in TE and EE, indicating that a powerful test of this scenario is anticipated with near-future data from ACT and other ground-based experiments.

Cosmology is one of the four science pillars of LSST, which promises to be transformative for our understanding of dark energy and dark matter. The LSST Dark Energy Science Collaboration (DESC) has been tasked with deriving constraints on cosmological parameters from LSST data. Each of the cosmological probes for LSST is heavily impacted by the choice of observing strategy. This white paper is written by the LSST DESC Observing Strategy Task Force (OSTF), which represents the entire collaboration, and aims to make recommendations on observing strategy that will benefit all cosmological analyses with LSST. It is accompanied by the DESC DDF (Deep Drilling Fields) white paper (Scolnic et al.). We use a variety of metrics to understand the effects of the observing strategy on measurements of weak lensing, large-scale structure, clusters, photometric redshifts, supernovae, strong lensing and kilonovae. In order to reduce systematic uncertainties, we conclude that the current baseline observing strategy needs to be significantly modified to result in the best possible cosmological constraints. We provide some key recommendations: moving the WFD (Wide-Fast-Deep) footprint to avoid regions of high extinction, taking visit pairs in different filters, changing the 2x15s snaps to a single exposure to improve efficiency, focusing on strategies that reduce long gaps (>15 days) between observations, and prioritizing spatial uniformity at several intervals during the 10-year survey.