Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

TL;DR

This paper explores torsional birefringence effects in metric-affine Chern-Simons gravity, analyzing cosmological solutions and gravitational wave propagation, revealing birefringence and the behavior of tensor and scalar modes.

Contribution

It provides analytical solutions for torsion and nonmetricity in a cosmological setting and studies gravitational wave polarization effects in this modified gravity theory.

Findings

Tensor modes couple to torsion, causing birefringence with different dispersion for polarizations.

Purely tensor torsion propagates as a wave, while nonmetricity acts like a harmonic oscillator.

Scalar modes decay exponentially and do not propagate.

Abstract

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, characterized by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.