First evidence of running cosmic vacuum: challenging the concordance
  model
  Despite the fact that a rigid $\Lambda$-term is a fundamental building block
of the concordance $\Lambda$CDM model, we show that a large class of
cosmological scenarios with dynamical vacuum energy density $\rho_{\Lambda}$
and/or gravitational coupling $G$, together with a possible non-conservation of
matter, are capable of seriously challenging the traditional phenomenological
success of the $\Lambda$CDM. In this paper, we discuss these "running vacuum
models" (RVM's), in which $\rho_{\Lambda}=\rho_{\Lambda}(H)$ consists of a
nonvanishing constant term and a series of powers of the Hubble rate. Such
generic structure is potentially linked to the quantum field theoretical
description of the expanding Universe. By performing an overall fit to the
cosmological observables $SNIa+BAO+H(z)+LSS+BBN+CMB$ (in which the WMAP9,
Planck 2013 and Planck 2015 data are taken into account), we find that the
class of RVM's appears significantly more favored than the $\Lambda$CDM, namely
at an unprecedented level of $\gtrsim4.2\sigma$. Furthermore, the Akaike and
Bayesian information criteria confirm that the dynamical RVM's are strongly
preferred as compared to the conventional rigid $\Lambda$-picture of the cosmic
evolution.
