Big-Bounce in projectively invariant Nieh-Yan models: the Bianchi I case

TL;DR

This paper extends the Nieh-Yan topological invariant to metric-affine gravity, demonstrating its role in enabling bouncing cosmological solutions in Bianchi I models without singularities.

Contribution

It introduces a generalized Nieh-Yan term that restores topologicity and projective invariance in nonmetricity contexts, and applies it to modified gravity theories with bouncing cosmologies.

Findings

Bouncing solutions in Bianchi I models are derived.

Finite time singularities are analyzed and found not to spoil geodesic completeness.

Scalar perturbations remain regular in these bouncing space-times.

Abstract

We show that the Nieh-Yan topological invariant breaks projective symmetry and loses its topological character in presence of non vanishing nonmetricity. The notion of the Nieh-Yan topological invariant is then extended to the generic metric-affine case, defining a generalized Nieh-Yan term, which allows to recover topologicity and projective invariance, independently. As a concrete example a class of modified theories of gravity is considered and its dynamical properties are investigated in a cosmological setting. In particular, bouncing cosmological solutions in Bianchi I models are derived. Finite time singularities affecting these solutions are analysed, showing that the geodesic completeness and the regular behavior of scalar perturbations in these space-times are not spoiled.