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

TL;DR

We study gravitational waves in a Palatini gravity framework with a non-minimal geometry–matter coupling mediated by contractions $X=R_{ mu}T^{ mu}$ and $Y=g^{ mu u}R^{ ho}{}_{ mu  nu}T_{ ho}{}^{ sigma}$. Varying the action, the connection is solved algebraically in terms of derivatives of $T_{ mu u}$, leading to an effective metric equation where the standard wave operator acts on the metric perturbation plus an extra operator acting on the energy–momentum tensor. Linearized analysis on a Minkowski background shows that, after appropriate gauge choices and in the limit of vanishing hypermomentum, the tensor GW equation acquires a modified source term, effectively producing two dispersion branches for GWs propagating in matter. In the kinetic theory treatment, the GW–matter interaction is encoded in a dielectric function, yielding a Landau-damping–like band structure with a wavenumber cut-off $k_0$ tied to the coupling to the co-Ricci tensor; however, cosmological bounds from Newtonian limits imply that the degenerate regime is not accessible in late-time dark matter, and realistic 100 Hz GW signals are not damped in this framework. The results highlight how geometry–matter couplings in metric–affine theories can imprint observable signatures on GW propagation and motivate further numerical and astrophysical investigations in dense media or different epochs.

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.

Figures (2)

• Figure 1: Propagation for the branch $\omega_{r,+}$ for $\forall\;k$
• Figure 2: Propagation for the branch $\omega_{r,-}$ for $k^2>k_0^2$