Stringy-running-vacuum-model inflation: from primordial gravitational waves and stiff axion matter to dynamical dark energy

Abstract

In previous works, we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this “stringy RVM” version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a ‘stiff’ gravitational axion “matter”, which in turn couples to the gravitational anomaly terms, assumed to be non-trivial at early epochs. In the presence of primordial gravitational wave (GW) perturbations, such anomalous couplings lead to an RVM-like dynamical inflation, without external inflatons. We review here this framework and discuss potential scenarios for the generation of such primordial GW, among which the formation of unstable domain walls, which eventually collapse in a non-spherical-symmetric manner, giving rise to GW. We also remark that the same type of “stiff” axionic matter could provide, upon the generation of appropriate potentials during the post-inflationary eras, (part of) the Dark Matter (DM) in the Universe, which could well be ultralight, depending on the parameters of the string-inspired model. All in all, the new (stringy) mechanism for RVM inflation preserves the basic structure of the original (and more phenomenological) RVM, as well as its main advantages: namely, a mechanism for graceful exit and for generating a huge amount of entropy capable of explaining the horizon problem. It also predicts axionic DM and the existence of mild dynamical Dark Energy (DE) of quintessence type in the present universe, both being “living fossils” of the inflationary stages of the cosmic evolution. Altogether the modern RVM appears to be a theoretically sound (string-based) approach to cosmology with a variety of phenomenologically testable consequences.

Multi-fluid cosmology in Einstein gravity: analytical solutions

“…A stiff fluid can also mimic anisotropy in the universe [220,222,293,298,367]. Finally, certain string-inspired effective gravitational field theories of the primordial universe [42][43][44]285,286] contain a massless Kalb-Ramond axion of gravitational nature which is equivalent to an effective fluid with a stiff equation of state, and other stringy axions are possible. These fields are linked to matter-antimatter asymmetry in the universe after inflation and to axionic dark matter.…”

“…These fields are linked to matter-antimatter asymmetry in the universe after inflation and to axionic dark matter. It is speculated that a stiff matter era precedes inflation in these theories [286].…”

Torsion in String-Inspired Cosmologies and the Universe Dark Sector

“…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].…”

“…Torsion constitutes therefore a rather vast research area, rich in physical applications (albeit not yet confirmed experimentally), as, we hope, becomes clear from the above introduction, and hence cannot be reviewed in all of its aspects in this short review. Here there shall be a focus instead on only a particular kind of torsion, already mentioned previously, namely the one which stems from the antisymmetric tensor field of the bosonic massless gravitational multiplet of the string [25,26,67], and shall discuss its connection with the dark sector of the universe in the context of a low-energy string-inspired cosmology with non-trivial gravitational anomalies [95] at early epochs of the universe [62][63][64][65]. The anomalous terms are expressed by the presence in the Lagrangian of a CP-violating gravitational Chern-Simons term [20,21] coupled to the string-model independent KR axion, which in (3 + 1)-dimensional space times is dual to the torsion in a way we shall explain in detail.…”

The accelerating universe: evidence and theories

“…Mavromatos and Peracaula [24] espouse the idea that the fields from the gravity multiplet of string theory, namely the graviton, the dilaton and the axion can explain the acceleration both during the epoch of inflation and in the present epoch. In this Running Vacuum Model they explain all epochs of cosmological evolution from relics of string theory.…”