Relaxing the $\sigma_8$-tension through running vacuum in the Universe

TL;DR

This paper demonstrates that running vacuum models can better fit cosmological data, especially addressing the $\sigma_8$-tension, and support the idea of dynamical dark energy over the standard $\Lambda$CDM model.

Contribution

It shows how running vacuum models relax the $\sigma_8$-tension and improve the fit to large scale structure data compared to $\Lambda$CDM.

Findings

Running vacuum models fit LSS data better than $\Lambda$CDM.

They successfully relax the $\sigma_8$-tension.

Dynamical dark energy may be encoded in current observations.

Abstract

It has recently been shown that the class of running vacuum models (RVMs) has the capacity to fit the overall cosmological observations better than the concordance $\Lambda$CDM model, therefore supporting the possibility of dynamical dark energy (DE). Apart from the cosmic microwave background (CMB) anisotropies, the most crucial datasets involved are: i) baryonic acoustic oscillations (BAO), and ii) direct large scale structure (LSS) formation data. Analyses mainly focusing on CMB and with insufficient BAO+LSS input generally fail to capture the dynamical DE signature, whereas the few existing studies accounting for the wealth of known CMB+BAO+LSS data (see in particular Sol\`a, G\'omez-Valent \& de Cruz P\'erez 2015, 2017; and Zhao et al. 2017) do converge to the remarkable conclusion that dynamical DE might well be encoded in the current cosmological observations at a $3-4\sigma$ c.l. A decisive factor is the persistent $\sigma_8$-tension between the $\Lambda$CDM and the data. Because the issue is obviously pressing, we devote this work to explain how and why running vacuum in the expanding universe successfully relaxes the existing $\sigma_8$-tension and describes the LSS formation data significantly better than the $\Lambda$CDM.