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

Abstract

Abstract. Next year we will celebrate 100 years of the cosmological term, Λ, 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 non-vanishing, positive, Λ-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 Λ. In particular, we are still facing the crucial question whether Λ 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 Λ =const. 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 Λ = Λ(H) is a function of the Hubble rate -against the "concordance" ΛCDM model. The support is at an unprecedented level of 4σ 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.

Running vacuum in the Universe and the time variation of the fundamental constants of Nature

“…According to [49], the data show a preference (at the level of 3σ ) for a dynamical vacuum of the form (11) rather than the rigid vacuum (ν = 0) of the CDM case, for which ρ = const. The obtained fit values of the vacuum parameter ν stay in the ballpark of 10 −3 [48,59,60], and therefore we can use this order of magnitude determination as a characteristic input in our estimate of the variation of the fundamental constants. The predicted mass drift rates are indicated in Figs.…”

“…The obtained result for the vacuum energy density can be motivated from the integration of the renormalization group (RG) flow associated to the Hubble expansion, within the context of the running vacuum model (RVM)-see [45][46][47][48][49][50] and the references therein. Let us note that the leading RG effects up to order ∼ H 4 take on the form of the power series [47] …”

“…In order to estimate quantitatively these effects within the RVM, we take as a basis the numerical fit estimates obtained in [49,50,59,60] using the known data on SNIa+BAO+H(z)+LSS+BBN+CMB -see also [48] for a review. Among these observational sources (which involve several hundreds of data points indicated in these references) we use 36 data points on the Hubble rate H (z) at different redshifts in the range 0 < z ≤ 2.36, as compiled in [77,78], out of which 26 data points are inferred from the differential age method, whereas 10 correspond to measures obtained from the baryonic acoustic oscillation method (cf.…”

“…These are the so-called running vacuum models (RVMs) of the cosmological evolution; see e.g. [44] for a recent summarized discussion and [45][46][47][48] for a more extensive review and a comprehensive list of references. In these models there are no ultralight scalar fields and the time variation of the fundamental constants is effectively triggered via quantum effects induced by the cosmological renormalization group, whose flow is naturally set up by the expansion rate H , cf.…”

“…The framework is characterized by a dynamical vacuum energy density, ρ , which is a power series of H and its time derivatives. For the current Universe, it suffices to consider ρ = ρ (H,Ḣ ) up to linear terms inḢ and quadratic in H [47][48][49][50][51]. However, extensions with higher powers have also been considered for describing inflation; see [47,52] and [53][54][55][56][57] for different kind of scenarios, including anomaly-induced inflation [58].…”