Gravitational wave propagation in generalized hybrid metric-Palatini gravity

TL;DR

GHMPG extends f(R) gravity by allowing a generalized dependence on both the metric and Palatini scalars via two fields $\varphi$ and $\psi$ with potential $V(\varphi,\psi)$. The tensor sector remains massless and propagates at speed of light, while two scalar modes emerge as coupled massive fields that can be diagonalized into two Klein-Gordon modes with masses $M_\Phi^2$ and $M_\Psi^2$, potentially tunable to zero. Polarization content is analyzed with the Newman-Penrose formalism, showing tensor polarizations match GR in the massless limit, while scalar polarizations (longitudinal and breathing) arise from a single scalar degree of freedom and can be affected by mass; vector modes are suppressed in plane-wave propagation. Cosmological and solar-system constraints drive the scalar fields to near-constant values today, greatly suppressing scalar modes and making GW propagation effectively GR-like, implying the GHMPG remains, in this regime, unfalsifiable by GW tests, though future detectors with enhanced scalar-mode sensitivity could probe residual effects.

Abstract

In this work we analyze the propagation properties of gravitational waves in the hybrid metric-Palatini gravity theory. We introduce the scalar-tensor representation of the theory to make explicit the scalar degrees of freedom of the theory and obtain their equations of motion in a form decoupled from the metric tensor. Then, we introduce linear perturbations for the metric tensor and for the two scalar fields and obtain the propagation equations for these three quantities. We analyzed the theory both at non-linear and at linear level through the Newman-Penrose formalism so to find the polarization states. We show that the tensor modes propagate at the speed of light and feature the usual +- and x-polarization modes also present in General Relativity (GR), plus two additional polarization modes: a longitudinal mode and a breathing mode, described by the same additional degree of freedom. On the other hand, the theory features two additional scalar modes not present in GR. These modes are massive and, thus, propagate with a speed smaller than the speed of light in general. The masses of the scalar modes depend solely on the interaction potential between the two scalar fields in the theory, which suggests that one can always fine-tune the potential to make the scalar modes massless and reduce their propagation speed to the speed of light. Given the possibility of fine-tuning the theory to match the observational predictions of GR and in the absence of any measured deviations, these features potentially render the hybrid metric-Palatini theory unfalsifiable in the context of gravitational wave propagation.