Torsion in String-Inspired Cosmologies and the Universe Dark Sector

Abstract

Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed. It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the “Running-Vacuum-Model (RVM)” cosmological framework, without fundamental inflaton fields. The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four-dimensional string universe (after compactification). The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models. Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made.

Going beyond the Standard paradigm of Cosmology: Torsion, gravitational anomalies and inflation without inflaton fields

“…In the presence of such black holes, the gravitational anomaly terms are therefore non trivial. The same is true when one has GW, which could be the result of either coalescence of such primordial Kerr black holes [12], or the non-spherical collapse of unstable domain walls [19] arising from the non-degenerate gravitino-condensate potential due to percolation effects, as mentioned above [38,39]. When such GW are produced in abundant quantities, they may condense, which can then lead to inflation of an RVM type, without inflaton fields, as we now proceed to discuss [19,20].…”

“…It can be shown [31][32][33] that the H 𝜇𝜈𝜌 , which the effective string-inspired gravitational action depends upon, due to the abelian gauge symmetry 𝐵 𝜇𝜈 → 𝐵 𝜇𝜈 + 𝜕 𝜇 𝜃 (𝑥) 𝜈 − 𝜕 𝜈 𝜃 (𝑥) 𝜇 that characterises the closed string sector [2,40], can be viewed as a totally antisymmetric torsion, and this interpretation holds up to and including O (𝛼 ) terms in the effective action. For a general discussion and comparison of this model with others in contorted geometries we refer the reader to [12], and references therein. The GS Chern-Simons countertems, appearing in the definition of H , are required in string theory for gauge and gravitational anomaly cancellation in the higher-dimensional theory.…”

“…where we used the fact that the Chern-Simons gravitational anomaly terms are total derivatives 𝑅 𝜇𝜈𝜌 𝜎 𝑅 𝜇𝜈𝜌 𝜎 = K 𝜇 (𝜔) ; 𝜇 , with ; denoting the gravitational covariant derivative with respect to the (torsion-free) spin connection 𝜔 (it can be shown that H -torsion terms can be removed from the anomaly by appropriate counterterms, see discussion and references in [12]). The tilde denotes the gravitational dual of the Riemann tensor.…”

“…The quantity 𝑏(𝑡 0 ) is a boundary condition for the KR axion field at the onset of the second (RVM) inflation, at 𝑡 = 𝑡 0 > 0 (assuming the Big Bang occurring at 𝑡 = 0). The requirement of the satisfaction of the transplanckian conjecture, that is, no modes with momenta higher than the Planck scale appear in the spectrum, including gravitons, and hence the UV cutoff 𝜇 in (2) is at most of order of the Planck scale, in conjunction with the slow-roll condition for the 𝑏(𝑥) axion, imply the allowed range of the string mass scale [12,19]: 2.6 × 10 −5 𝑀 Pl 𝑀 𝑠 ≤ 10 −3 𝑀 Pl . On average, one may therefore take 𝑀 𝑠 = O (10 −3 ) 𝑀 Pl , implying 𝜇 = O (𝑀 Pl ), which is natural.…”

“…In this talk, which is based on material presented in [11,12], I will additionally motivate going beyond ΛCDM by the desire: (i) to answer microscopically the question whether inflation [13] is due to external fundamental scalar inflaton fields, or, like the phenomenologically successful Starobinsky model [14], is a consequence of non-linear gravitational dynamics, which may involve a hidden scalar mode, and (ii) to understand in a geometrical way the observed matter-antimatter asymmetry in the Universe [15], which in the conventional particle physics framework is believed to be due to CP Violation in the early Universe, along with Baryon-number and C violation, as well as departure from thermal equilibrium (the celebrated Sakharov's conditions [16]).…”