Gravitational and chiral anomalies in the running vacuum universe and matter-antimatter asymmetry

Abstract

We present a model for the Universe in which quantum anomalies are argued to play an important dual rôle: they are responsible for generating matter-antimatter asymmetry in the Cosmos, but also provide time-dependent contributions to the vacuum energy density of "running-vacuum" type, which drive the Universe evolution. According to this scenario, during the inflationary phase of a string-inspired Universe, and its subsequent exit, the existence of primordial gravitational waves induce gravitational anomalies, which couple to the (Kalb-Ramond (KR)) axion field emerging from the antisymmetric tensor field of the massless gravitational multiplet of the string. Such anomalous CP violating interactions have two important effects: first, they lead to contributions to the vacuum energy density of the form appearing in the "running vacuum model" (RVM) framework, which are proportional to both, the square and the fourth power of the effective Hubble parameter, H 2 and H 4 respectively. The H 4 terms may lead to inflation, in a dynamical scenario whereby the rôle of the inflaton is played by the effective scalar-field ("vacuumon") representation of the RVM. Second, there is an undiluted KR axion at the end of inflation, which plays an important rôle in generating matter-antimatter asymmetry in the Cosmos, through baryogenesis via leptogenesis in models involving heavy right handed neutrinos. As the Universe exits inflation and enters a radiation dominated era, the generation of chiral fermionic matter is responsible for the cancellation of gravitational anomalies, thus restoring diffeomorphism invariance for the matter/radiation (quantum) theory, as required for consistency. Chiral U(1) anomalies may remain uncompensated, though, during matter/radiation dominance, providing RVM-like H 2 and H 4 contributions to the Universe energy density. Finally, in the current era, when the Universe enters a de Sitter phase again, and matter is no longer dominant, gravitational anomalies resurface, leading to RVM-like H 2 contributions to the vacuum energy density, which are however much more suppressed, as compared to their counterparts during inflation, due to the smallness of the present era's Hubble parameter H 0 . In turn, this feature endows the observed dark energy with a dynamical character that follows the RVM pattern, a fact which has been shown to improve the global fits to the current cosmological observations as compared to the concordance ΛCDM with its rigid cosmological constant , Λ > 0. Our model favours axionic Dark Matter, the source of which can be the KR axion. The uncompensated chiral anomalies in late epochs of the Universe are argued to play an important rôle in this, in the context of cosmological models characterised by the presence of large-scale cosmic magnetic fields at late eras.

Particle and entropy production in the running vacuum universe

“…Such dynamical interplay between the vacuum and matter is responsible for the nontrivial nature of the RVM as a generalized form of the ΛCDM in which the cosmological constant is replaced by a dynamical function of the Hubble rate which affects the entire cosmic history. We have remarked that these powers of the Hubble rate can be the generic result of the low-energy effective action based on the bosonic gravitational multiplet of string theory, as shown recently [68,69]. The presence of the gravitational Chern-Simons term associated with that action turns out to lead to an effective ∼ H 4 behavior when averaged over the inflationary spacetime.…”

“…Apart from its possible connection to QFT in curved spacetime in different frameworks [63][64][65]] -see also [66] for a review -it has recently been shown that the presence of the term H 4 in the effective expression of the vacuum energy density, Eq. (IV.2), can be the generic result of the low-energy effective action based on the bosonic gravitational multiplet of string theory, see [68]. The unavoidable presence of the (CP-violating) gravitational Chern-Simons term associated with that action turns out to lead to an effective ∼ H 4 behavior when averaged over the inflationary spacetime, in the presence of primordial gravitational waves.…”

“…In the early universe, before and during inflation, it is assumed that only fields from the gravitational multiplet of the string exist, which implies that the relevant bosonic part of the effective action pertinent to the dynamics of the inflationary period is given by [68]…”

“…We refer the reader to Ref. [68] for the technical details and specialized references, and to [69] for a summary of the underlying framework. Here we will focus only on the thermodynamical aspects of the cosmic evolution with a vacuum energy density of the form (IV.2) containing both the H 4 and H 2 dynamical components.…”

“…Along these lines we have the idea of the 'running vacuum model' (RVM), see [66,67] and references therein. Recently, a possible connection of the latter with the effective action of the bosonic gravitational multiplet of string theory has been put forward [68,69]. Within the RVM one can construct unified models of the cosmological evolution, in which vacuum plays a dynamical role with matter.…”