Gravitational waves in Palatini gravity for a non-minimal geometry-matter coupling

TL;DR

This paper explores how non-minimal geometry-matter couplings in Palatini gravity affect gravitational wave propagation, revealing potential subluminal speeds, damping effects, and frequency cut-offs due to non-Riemannian spacetime features.

Contribution

It introduces a framework for analyzing gravitational waves in non-Riemannian spacetime with non-minimal couplings, highlighting new effects like subluminal velocities and propagation cut-offs.

Findings

Tensor polarizations can have subluminal phase velocities.

Propagation can be damped in certain medium and coupling configurations.

Frequency spectrum exhibits cut-off scales due to geometric-matter interactions.

Abstract

We discuss the propagation of gravitational waves over a non-Riemannian spacetime, when a non-minimal coupling between the geometry and matter is considered in the form of contractions of the energy momentum tensor with the Ricci and co-Ricci curvature tensors. We focus our analysis on perturbations on a Minkowski background, elucidating how derivatives of the energy momentum tensor can sustain non-trivial torsion and non-metricity excitations, eventually resulting in additional source terms for the metric field. These can be reorganized in the form of D'Alembert operator acting on the energy momentum tensor and the equivalence principle can be reinforced at the linear level by a suitable choice of the parameters of the model. We show how tensor polarizations can exhibit a subluminal phase velocity in matter, evading the constraints found in General Relativity, and how this allows for the kinematic damping in specific configurations of the medium and of the geometry-matter coupling. These in turn define regions in the wavenumber space where propagation is forbidden, leading to the appearance of typical cut-off scale in the frequency spectrum.