The $H_0$ and $\sigma_8$ tensions and the scale invariant spectrum

TL;DR

This paper investigates the tensions in cosmological parameters like $H_0$ and $\sigma_8$ by analyzing various datasets, finding that the preference for a scale-invariant spectrum depends on the specific BAO data used, with implications for early universe physics.

Contribution

It extends previous analyses by incorporating joint CMB, HST, BAO, cluster counts, and weak lensing data to assess the viability of a scale-invariant spectrum model in explaining cosmological tensions.

Findings

CMB+HST+BAO 2PCF data disfavors the scale-invariant model compared to $ m{ extLambda CDM}$.

CMB+HST+BAO 2PACF data favors the scale-invariant model even with additional datasets.

Results highlight the dependence of model preference on the choice of BAO data analysis method.

Abstract

In a previous communication we showed that a joint analysis of Cosmic Microwave Background (CMB) data and the current measurement of the local expansion rate favours a model with a scale invariant spectrum (HZ) over the minimal $\Lambda$CDM scenario provided that the effective number of relativistic degrees of freedom, $N_{eff}$, is taken as a free parameter. Such a result is basically obtained due to the Hubble Space Telescope (HST) value of the Hubble constant, $H_0 = 73.24 \pm 1.74$ $\rm{km.s^{-1}.Mpc^{-1}}$ (68\% C.L.), as the CMB data alone discard the HZ+$N_{eff}$ model. Although such a model is not physically motivated by current scenarios of the early universe, observations pointing to a scale invariant spectrum may indicate that the origin of cosmic perturbations lies in an unknown physical process. Here, we extend the previous results performing a Bayesian analysis using joint CMB, HST, and Baryon Acoustic Oscillations (BAO) measurements. In order to take into account the well-known tension on the value of the fluctuation amplitude parameter, $\sigma_8$, we also consider Cluster Number counts (CN) and Weak Lensing (WL) data. We use two different samples of BAO data, which are obtained using two-point spatial (BAO 2PCF) and angular (BAO 2PACF) correlation functions. Our results show that a joint CMB+HST+BAO 2PCF analysis discards the HZP$+N_{eff}$ model with respect to the minimal $\Lambda$CDM scenario whereas the combination CMB+HST+BAO 2PACF favours the former model, even when an extended dataset with NC and WL is considered.