Torsion-induced axions in string theory, quantum gravity and the cosmological tensions

We discuss the role of torsion in string theory on inducing pseudoscalar degrees of freedom (axions), which in turn couple to (gravitational) Chern-Simons (CS) anomalous terms. Such interactions can induce inflation, of running vacuum type, not requiring external inflaton fields, through condensation of the anomalous terms as a consequence of primordial chiral gravitational-wave (GW) tensor perturbations in a weak-quantum gravity setting. The presence of an UV cutoff for the GW quantum graviton modes opens up the system, leading to a dissipative behaviour realised via the presence of non trivial imaginary parts of the gravitational CS terms. The naive estimate of the life time of inflation based on such imaginary parts, which afflict the pertinent GW Hamiltonian, is quite consistent with the estimates of the duration of inflation based on an analysis of the condensate-induced linear-axion-potential by means of dynamical systems. Such quantum-gravity effects can also contribute positively to the alleviation of cosmological tensions if they survive today. In the talk we discuss the conditions under which such a result may be achieved. We also discuss the potential role of other axions in string theory, coming from compactification, in inducing enhanced densities of primordial black holes during RVM inflation, thereby contributing to significantly increased percentages of these black holes that can play the role of dark matter components. Moreover, under certain circumstances, that we shall discuss in some detail, it is also possible that the initially massless torsion-induced axions can acquire a non-trivial mass during the radiation era, thereby providing additional dark matter components in the Universe. With regards to this aspect, we also emphasise the role of massive right-handed neutrinos, provided that such excitations exist in the relevant spectra.