The H0 and σ8 tensions and the scale invariant spectrum

In a previous communication [1] it was shown 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 (HZP) over the minimal ΛCDM scenario provided that the effective number of relativistic degrees of freedom, Neff, is taken as a free parameter. Such a result is basically obtained due to the Hubble Space Telescope (HST) value of the Hubble constant, H0 = 73.24 ± 1.74 km . s−1.Mpc−1 (68% C.L.), as the CMB data alone discard the HZP+Neff 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, σ8, 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 the joint CMB+HST+WL+NC dataset favor the extensions of the ΛCDM model over its minimal parameterization. Also, analysis with the BAO 2PCF always discard the HZP+Neff model with respect to standard scenario, whereas the combinations using BAO 2PACF favor the former model. We, therefore, find that all dataset disfavor the ΛCDM model with respect to the HZP+Neff extension, the only exception being the joint analysis with BAO (2PCF).