# The $H_0$ tension in light of vacuum dynamics in the Universe

## TL;DR

This paper explores how the running vacuum model (RVM), which allows vacuum energy to depend on the universe's expansion rate, can help resolve the persistent $H_0$ tension by fitting various cosmological observations better than the standard $\\Lambda$CDM model.

## Contribution

It demonstrates that the RVM can alleviate the $H_0$ tension and improve fit quality to multiple cosmological data sets compared to the standard model.

## Key findings

- RVM favors CMB-derived $H_0$ values over local measurements.
- RVM predicts smaller $\sigma_8(0)$, aligning better with large-scale structure data.
- RVM provides a better overall fit to cosmological observations than $\\Lambda$CDM.

## Abstract

Despite the outstanding achievements of modern cosmology, the classical dispute on the precise value of $H_0$, which is the first ever parameter of modern cosmology and one of the prime parameters in the field, still goes on and on after over half a century of measurements. Recently the dispute came to the spotlight with renewed strength owing to the significant tension (at $>3\sigma$ c.l.) between the latest Planck determination obtained from the CMB anisotropies and the local (distance ladder) measurement from the Hubble Space Telescope (HST), based on Cepheids. In this work, we investigate the impact of the running vacuum model (RVM) and related models on such a controversy. For the RVM, the vacuum energy density $\rho_{\Lambda}$ carries a mild dependence on the cosmic expansion rate, i.e. $\rho_{\Lambda}(H)$, which allows to ameliorate the fit quality to the overall $SNIa+BAO+H(z)+LSS+CMB$ cosmological observations as compared to the concordance $\Lambda$CDM model. By letting the RVM to deviate from the vacuum option, the equation of state $w=-1$ continues to be favored by the overall fit. Vacuum dynamics also predicts the following: i) the CMB range of values for $H_0$ is more favored than the local ones, and ii) smaller values for $\sigma_8(0)$. As a result, a better account for the LSS structure formation data is achieved as compared to the $\Lambda$CDM, which is based on a rigid (i.e. non-dynamical) $\Lambda$ term.