Running vacuum against the $H_0$ and $\sigma_8$ tensions

Understand

The cosmological term, $\Lambda$, was introduced $104$ years ago by Einstein in his gravitational field equations.

• Whether $\Lambda$ 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, $\rho_{\rm vac}$, 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 (RVM's).