Cosmological constant vis-à-vis dynamical vacuum: Bold challenging the ΛCDM

Abstract

Next year we will celebrate 100 years of the cosmological term, [Formula: see text], in Einstein’s gravitational field equations, also 50 years since the cosmological constant problem was first formulated by Zeldovich, and almost about two decades of the observational evidence that a nonvanishing, positive, [Formula: see text]-term could be the simplest phenomenological explanation for the observed acceleration of the Universe. This mixed state of affairs already shows that we do no currently understand the theoretical nature of [Formula: see text]. In particular, we are still facing the crucial question whether [Formula: see text] is truly a fundamental constant or a mildly evolving dynamical variable. At this point the matter should be settled once more empirically and, amazingly enough, the wealth of observational data at our disposal can presently shed true light on it. In this short review, I summarize the situation of some of these studies. It turns out that the [Formula: see text]. hypothesis, despite being the simplest, may well not be the most favored one when we put it in hard-fought competition with specific dynamical models of the vacuum energy. Recently, it has been shown that the overall fit to the cosmological observables SNIa+BAO+H(z)+LSS+BBN+CMB do favor the class of “running” vacuum models (RVM’s) — in which [Formula: see text] is a function of the Hubble rate — against the “concordance” [Formula: see text]CDM model. The support is at an unprecedented level of [Formula: see text] and is backed up with Akaike and Bayesian criteria leading to compelling evidence in favor of the RVM option and other related dynamical vacuum models. I also address the implications of this framework on the possible time evolution of the fundamental constants of Nature.