Running vacuum against the H0 and σ8 tensions

The cosmological term, Lambda, was introduced 104 years ago by Einstein in his gravitational field equations. Whether. is a rigid quantity or a dynamical variable in cosmology has been a matter of debate for many years, especially after the introduction of the general notion of dark energy (DE). Lambda is associated to the vacuum energy density, rho(vac), and one may expect that it evolves slowly with the cosmological expansion. Herein we present a devoted study testing this possibility using the promising class of running vacuum models (RVMs). We use a large string SNIa+BAO+H(z)+LSS+CMB of modern cosmological data, in which for the first time the CMB part involves the full Planck 2018 likelihood for these models. We test the dependence of the results on the threshold redshift z(*) at which the vacuum dynamics is activated in the recent past and find positive signals up to similar to 4.0 sigma for z(*) similar or equal to 1. The RVMs prove very competitive against the standard Lambda CDM model and give a handle for solving the sigma(8) tension and alleviating the H-0 one. Copyright (C) 2021 EPLA