Running vacuum against the H ₀ and σ₈ tensions

Abstract

The cosmological term, Λ, was introduced 104 years ago by Einstein in his gravitational field equations. Whether Λ is a rigid quantity or a dynamical variable in cosmology has been a matter of debate for many years, especially after the introduction of the general notion of dark energy (DE). Λ is associated to the vacuum energy density, , and one may expect that it evolves slowly with the cosmological expansion. Herein we present a devoted study testing this possibility using the promising class of running vacuum models (RVMs). We use a large string SNIa+BAO+H(z)+LSS+CMB of modern cosmological data, in which for the first time the CMB part involves the full Planck 2018 likelihood for these models. We test the dependence of the results on the threshold redshift at which the vacuum dynamics is activated in the recent past and find positive signals up to for . The RVMs prove very competitive against the standard ΛCDM model and give a handle for solving the tension and alleviating the H 0 one.

Torsion in String-Inspired Cosmologies and the Universe Dark Sector

“…What we shall discuss, though, is how the RVM framework in the modern era can contribute to observable, in principle, deviations from the ΛCDM [51,52,56,57,59], and most importantly alleviation of the current cosmological-data tensions H 0 and σ 8 [53][54][55]. In fact, as we shall discuss now, a slightly modified version of the conventional RVM, has the capacity of alleviating simultaneously the H 0 and σ 8 tensions [58].…”

“…However there is an even more important role of the RVM, which allows, as already mentioned, for a simultaneous alleviation of the H 0 and σ 8 tension [58]. To this end, one needs to consider a variant of RVM, called type-II RVM, which allows for a cosmic-time dependence of the gravitational constant:…”

“…which should be compared against the plethora of the available cosmological data [5,58]. It should be stressed that the function ϕ(t) is not the Brans-Dicke (BD) field, and the type-II RVM is defined only through the above modification (79), without ascribing a dynamical rolefor the function ϕ(t).…”

“…We mention at this point that one such theoretical framework is the so-called "Running Vacuum Model (RVM)" framework [44][45][46] (where a time-dependent vacuum energy is assumed, but with equation of state w vacuum = −1 as in the de Sitter case). This provides an effective smooth evolution of the universe, from inflation till the current era [47][48][49][50], with, in principle observable deviations from ΛCDM [51][52][53][54][55][56][57], which notably can also alleviate simultaneously both types of tensions, H 0 and σ 8 , in the current data [58,59] (for another model with dynamical, "running", dark energy, where the space-time is associated with a dynamical field (dynamical space time), and its phenomenological consequences, see [60,61]). In this review we shall derive such an RVM cosmology as an appropriate lowenergy limit of string theories, under some special circumstances that shall be discussed in detail [62][63][64][65].…”

“…Due to the link of the KR axion with torsion, then, one could have a geometrical origin of DM in such models. The RVM nature of this effective string-inspired cosmological model is maintained until the current era [62], and in this sense the model has observable in principle variations from the ΛCDM, contributing in parallel to the alleviation of the cosmological tensions in the data [51][52][53][54][55][56][57][58][59].…”