Dark torsion oscillations and bounces induced by Barbero-Immirzi and quantum correction on Einstein-Cartan gravity with very light inflatons

Abstract

In this paper we present several examples of how to constrain loop quantum gravity Barbero-Immirzi (BI) parameter, either by using quantum corrections in Nieh–Yan (NY) modified Einstein-Cartan (EC) gravity with the Holst term. The reason why we introduce some extra terms in the actions, is that even when one adds both NY and Holst terms, being topological terms, they do not contribute to the dynamics of the problem and to the equations of motion (EOM). Examples run from quantum corrections and torsion mass in the dark universe with very light inflaton approximation to bouncing cosmologies in NY gravity. This follows similar model from Tukhashvili and Steinhardt (2023) of a bouncing cosmology induced by torsion condensates in EC gravity. The Lagrangian in this paper, is shown to be expressed in terms of NY polynomial form. The quantum one-loop correction is taken in NY Lagrangian as the inverse of BI parameter. This has been recently appeared in He et al. (2024) quantum corrections in Einstein-Cartan-Nieh–Yan one loop quantum gravity in Starobinsky inflation. We show that to have a cosmological NY dark universe one needs a real BI parameter. Inflation Hubble scale of the order of O(100eV) and very light inflaton of mass ∼10−12TeV are used due to its relation with dark matter. The very light mass character of inflatons and much heavier torsion are responsible to induced cosmological bounce in dark universe. When one introduces the quantum correction parameter b as second-order in front of the NY topological term in squared and introduce the NY term back into the ECH gravity, the EC gravity limit where BI parameter β→∞, yields a chiral fermion density ρ5. This result lies very close to the upper bound in the range of 0≤β≤1.185, previously obtained by Panza et al. Analysis of fermionic currents shows that Holst term can be eliminated by choosing β=0.288. Massive torsion oscillates in Einstein-Cartan gravity in the BI limit of β→∞.