Possible signals of vacuum dynamics in the Universe
  We study a generic class of time-evolving vacuum models which can provide a
better phenomenological account of the overall cosmological observations as
compared to the $\Lambda$CDM. Among these models, the running vacuum model
(RVM) appears to be the most motivated and favored one, at a confidence level
of $\sim 3\sigma$. We further support these results by computing the Akaike and
Bayesian information criteria. Our analysis also shows that we can extract fair
signals of dynamical dark energy (DDE) by confronting the same set of data to
the generic XCDM and CPL parametrizations. In all cases we confirm that the
combined triad of modern observations on Baryonic Acoustic Oscillations, Large
Scale Structure formation, and the Cosmic Microwave Background, provide the
bulk of the signal sustaining a possible vacuum dynamics. In the absence of any
of these three crucial data sources, the DDE signal can not be perceived at a
significant confidence level. Its possible existence could be a cure for some
of the tensions existing in the $\Lambda$CDM when confronted to observations.
