Bouncing Cosmologies in modified gravity with space time torsion

TL;DR

The paper investigates whether a non-singular cosmological bounce can be realized in modified gravity with spacetime torsion by recasting $f(\bar{R})$ gravity in the Einstein frame as a scalar–tensor theory with derivative couplings between a scalar $\phi$ and a rank-2 torsion field $Z_{ab}$. In a strictly isotropic FRW background, three torsion-involved cases fail to produce a bounce without violating the null energy condition; however, relaxing to an inhomogeneous, mildly anisotropic spacetime enables a consistent bouncing solution (Case 2) with exact field solutions and a reconstructed $f(\bar{R})$ whose curvature is maximized at the bounce. The torsion fields decay over time, aligning with their absence in the present universe, and linear perturbations remain stable, with small anisotropy-induced corrections, while Planck data constrain the model parameters. Overall, the work suggests that a bounce can arise in torsion-extended gravity without exotic matter, provided one allows slight deviations from perfect isotropy.

Abstract

We explore the possibility of realizing a non-singular bounce in the early universe within the framework of modified gravity with spacetime torsion. In Einstein Cartan theory, torsion is embedded in the spacetime by adding an antisymmetric part in affine connection . We consider generalized version of the framework as $f(\bar{R})$, $\bar{R}$ being the scalar of the modified curvature tensor. $f(\bar{R})$ gravity is recast in Einstein frame as non-minimally coupled scalar tensor theory where the scalar field gets coupled with a rank 2 antisymmetric torsion field through derivative couplings. We investigate whether the introduction of three additional torsion-dependent terms in Einstein frame help to realize a bounce. We first explore this cosmological system in the background of a homogeneous and isotropic FRW spacetime but inclusion of the torsion terms are insufficient to produce a bounce in this symmetric setting. Motivated by this limitation, we relax the symmetry and generalize the background to include inhomogeneity and anisotropy. In this setup, the dynamics is modified in such a way that a bouncing solution is possible without invoking phantom fields or energy condition violations. We have found the exact solutions of all the fields and reconstructed the modified gravity form. We have addressed the behaviour of the fields under perturbation and investigated the stability of the solutions. Constraints on the model parameters have also been derived based on cosmological observations.