Geometrical origins of the universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter

Abstract

In a modest attempt to present potentially new paradigms in cosmology, including its inflationary epoch, and initiate discussions, I review in this article some novel, string-inspired cosmological models, which entail a purely geometrical origin of the dark sector of the Universe but also of its observed matter-antimatter asymmetry. The models contain gravitational (string-model independent, Kalb–Ramond (KR)) axion fields coupled to primordial gravitational anomalies via CP-violating interactions. The anomaly terms are four-space–time-dimensional remnants of the Green–Schwarz counterterms appearing in the definition of the field strength of the spin-one antisymmetric tensor field of the (bosonic) massless gravitational string multiplet, which also plays the role of a totally antisymmetric component of torsion. I show how in such cosmologies the presence of primordial gravitational waves can lead to anomaly condensates and dynamical inflation of a ‘running-vacuum-model’ type, without external inflatons, but also to leptogenesis in the radiation era due to anomaly induced Lorentz and CPT violating KR axion backgrounds. I also discuss how the torsion-related KR-axion could acquire a mass during the QCD epoch, thus playing the role of (a component of) dark matter. Phenomenological considerations of the inflationary and post-inflationary (in particular, modern) eras of the model are briefly discussed, including its potential for alleviating the observed tensions in the cosmological data of the current epoch. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.

The Cosmological Constant Problem and Running Vacuum in the Expanding Universe

“…The demonstration that RVM-inflation is a consequence of calculations within QFT in curved spacetime has been accomplished only very recently in [47], where the specific VED form (7.1) for inflation was explicitly derived. Worth noticing is also the existence of a string-inspired version of RVM-inflation (see [97,98], and particualry also [99] in this Theme Issue), in which inflation is triggered by gravitational anomalies through a mechanism of condensation of primordial gravitational waves in the very early universe, which is capable of engendering ∼ H 4 contributions to the VED. It is amusing to think of a double trigger for RVM-inflation from H 4 as well as from H 6 terms.…”

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

“…Moreover, they have the potential to alleviate the observed tensions in the data [36]. In fact, as argued in [11,12,19], in the stringy RVM context, quantum graviton fluctuations lead to logarithmically-dependent-on-𝐻 corrections to the conventional RVM, so that the vacuum energy density assumes the form 𝜌 stringyRVM 0 (𝐻) = 3𝜅 −2 𝑐 0 + 𝜈 + 𝑑 1 ln(𝑀 −2 Pl 𝐻 2 ) 𝐻 2 + . .…”

“…section 4). appropriately fixing N ch for a given coefficient of the gravitational Chern-Simons term in (1) (equivalently, for a given N ch , depending on the model, one fixes accordingly the coefficient of the Chern-Simons anomaly in (1) [11,12]). Such a cancellation ensures that the conventional Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology, where matter-radiation energy is conserved, holds for the post-RVM-inflationary epochs of the model.…”

“…For the range of the string scale found in our problem, one then obtains phenomenologically acceptable masses for the KR field, which could resemble the QCD axion, thus playing the rôle of an acceptable candidate for dark matter. In view of the connection of the 𝑏(𝑥) field to torsion, therefore, one may have a geometric origin of dark matter [11]. Other scenarios, however, exist, in which the KR axion develops complicated potentials that mix it with the other axions arising in string theory due to compactification [27], which can lead to an interesting and rich phenomenology [17], to be explored further in future works.…”

“…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]).…”