Current cosmological constraints on the scalar spectral index of primordial fluctuations $n_{\mathrm{s}}$ in the $\mathrm{\Lambda }$Vcold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model have excluded the minimal scale-invariant Harrison-Zel’dovich model ($n_{\mathrm{s}}=1$; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological data sets that, if not due to systematics, could indicate the presence of new physics beyond the $\mathrm{\Lambda }\mathrm{CDM}$ model. In light of these developments, we evaluate the Bayesian evidence against HZ in different data combinations and model extensions. Considering only the Planck temperature data, we find inconclusive evidence against HZ when including variations in the neutrino number $N_{\mathrm{eff}}$ and/or the helium abundance $Y_{\text{He}}$. Adding the Planck polarization data, on the other hand, yields strong evidence against HZ in the extensions we considered. Perhaps most interestingly, Planck temperature data combined with local measurements of the Hubble parameter [A. G. Riess et al., Astrophys. J. 826, 56 (2016); A. G. Riess et al. Astrophys. J. 861, 126 (2018)] give as the most probable model a HZ spectrum, with additional neutrinos. However, with the inclusion of polarization, standard $\mathrm{\Lambda }\mathrm{CDM}$ is once again preferred, but the HZ model with extra neutrinos is not strongly disfavored. The possibility of fully ruling out the HZ spectrum is therefore ultimately connected with the solution to current tensions between cosmological data sets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and a HZ spectrum could still offer a valid alternative.

• Received 24 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.063508