Bayesian Evidence against Harrison-Zel'dovich spectrum in tension cosmology

TL;DR

This paper evaluates Bayesian evidence against the Harrison-Zel'dovich spectrum in cosmology, considering dataset tensions and model extensions, and finds that the evidence depends on data combinations and assumptions, leaving room for new physics.

Contribution

It provides a comprehensive Bayesian analysis of the Harrison-Zel'dovich spectrum considering dataset tensions and model extensions, highlighting conditions under which it can still be viable.

Findings

Inconclusive evidence against HZ with Planck temperature data alone.

Strong evidence against HZ when including Planck polarization data.

HZ spectrum with extra neutrinos remains plausible when considering dataset tensions.

Abstract

Current cosmological constraints on the scalar spectral index of primordial fluctuations $n_{\rm s}$ in the $\Lambda$CDM model have excluded the minimal scale-invariant Harrison-Zel'dovich model ($n_{\rm s}=1$; hereafter HZ) at high significance, providing support for inflation. In recent years, however, some tensions have emerged between different cosmological datasets that, if not due to systematics, could indicate the presence of new physics beyond the $\Lambda$CDM model. In the 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 $N_{\rm eff}$ and/or the Helium abundance $Y_{\rm He}$. 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 constant give as the most probable model an HZ spectrum, with additional neutrinos. However, with the inclusion of polarisation, standard $\Lambda$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 datasets. If these tensions are confirmed by future data, then new physical mechanisms could be at work and an HZ spectrum could still offer a valid alternative.