Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case

TL;DR

This paper extends the Nieh-Yan invariant to metric-affine geometries, introduces a scalar field version in modified gravity, and demonstrates that Bianchi I cosmological models can avoid initial singularities through a big-bounce mechanism.

Contribution

It develops a new invariant in metric-affine gravity and applies it to cosmology, showing how it can lead to singularity-free bouncing solutions in Bianchi I models.

Findings

Initial singularity replaced by a big-bounce.

Solutions exhibit finite time singularities that do not affect geodesic completeness.

The Immirzi field's non-minimal coupling drives the bounce.

Abstract

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be independently accommodated by a suitable choice of the parameters featuring this new Nieh-Yan term. We then consider a special class of modified theories of gravity able to promote the Immirzi parameter to a dynamical scalar field coupled to the Nieh-Yan form, and we discuss in more detail the dynamics of the effective scalar tensor theory stemming from such a revised theoretical framework. We focus, in particular, on cosmological Bianchi I models and we derive classical solutions where the initial singularity is safely removed in favor of a big-bounce, which is ultimately driven by the non-minimal coupling with the Immirzi field. These solutions, moreover, turn out to be characterized by finite time singularities, but we show that such critical points do not spoil the geodesic completeness and wave regularity of these space-times.