An empirical investigation into cosmological tensions

TL;DR

This paper empirically investigates how modifications to the standard cosmological model, such as phantom dark energy and extra relativistic species, affect the tensions in Hubble constant and matter fluctuation amplitude, providing insights into potential solutions.

Contribution

It introduces an empirical approach analyzing specific non-standard cosmological parameters to understand their impact on key tensions without relying on free parameter variations.

Findings

Relations between $w$, $N_{eff}$ and $H_0$, $r_s$, $\sigma_8$ established

Empirical relation between $H_0$ and $\sigma_8$ derived

Insights into model characteristics that could resolve tensions

Abstract

The possibility that the $H_0$ tension is a sign of a physics beyond the $\Lambda$CDM model is one of the most exciting possibilities in modern cosmology. The challenge of solving this problem is complicated by several factors, including the worsening of the tension on $\sigma_8$ parameter when that on $H_0$ is raised. Furthermore, the perspective from which the problem is viewed should not be underestimated, since the tension on $H_0$ can also be interpreted as a tension on the size of the acoustic horizon, $r_s$, which deserves proper discussion. The common approach in the literature consists in proposing a new model that can resolve the tension and treat the new parameters of the theory as free in the analysis. However, allowing additional parameters to vary often results in larger uncertainties on the inferred cosmological parameters, causing an apparent relaxing in the tension due to the broaden in the posterior, instead of a genuine shift in the central value of $H_{0}$. To avoid this, we consider here an empirical approach that assumes specific non-standard values of the $\Lambda$CDM extensions and we analyze how the important parameters in the context of the tension vary accordingly. For our purposes, we study simple extensions of the standard cosmological model, such as a phantom DE component (with Equation of State $w < -1$) and extra relativistic species in the early Universe (so that $N_{eff} > 3.046$). We obtain relations between variation in the value of $w$ and $N_{eff}$ and changes in $H_0$, $r_s$ and $\sigma_8$. In this way an empirical relation between $H_0$ and $\sigma_8$ is provided, that is a first step in understanding which classes of theoretical models, and with which characteristics, could be able to break the correlation between the two tensions.