The $H_0$ and ${\sigma }_8$ tensions and the scale invariant spectrum

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, $H_0=73.24\pm 1.74$ $km.{\mathrm{s}}^{-1}.Mp{\mathrm{c}}^{-1}$ (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.

10 pages

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