Running Vacuum in the Universe: current phenomenological status
  I review the excellent phenomenological status of a class of dynamical vacuum
models in which the vacuum energy density, $\rho_{\Lambda}=\rho_{\Lambda}(H)$,
as a function of the Hubble rate, evolves through its interaction with dark
matter and/or through the accompanying running of the gravitational coupling
$G$, including the possibility of being self-conserved with a nontrivial
effective equation of state. Some of these models have been used to incorporate
into a single vacuum structure the rapid stage of inflation, followed by the
standard radiation and cold dark matter epochs all the way down until the dark
energy era. Remarkably, the running vacuum models (RVM's) render an outstanding
phenomenological description of the main cosmological data at a level that is
currently challenging the concordance $\Lambda$CDM model, thereby implying that
present observations seem to point to a running vacuum rather than to a rigid
cosmological constant $\Lambda$ in our Universe.
