Astrophysical Gravitational Waves in Conformal Gravity

TL;DR

This paper examines gravitational waves in conformal gravity models, showing they predict much weaker radiation than general relativity when explaining galaxy rotation curves without dark matter, thus constraining these models.

Contribution

It derives the linearized equations for conformal gravity, analyzes gravitational radiation from binaries, and constrains the models based on observational data, highlighting differences from general relativity.

Findings

Gravitational radiation in conformal gravity is significantly weaker than in GR for galaxy rotation curve explanations.

Conformal gravity models cannot account for binary orbital decay via gravitational waves, challenging their viability as dark matter alternatives.

In the large graviton mass limit, MCG reduces to GR, aligning with observed binary system behaviors.

Abstract

We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum gravity. Here we show that gravitational radiation emitted by compact binaries allows us to strongly constrain both models. We work in Weyl gauge, which fixes the rescaling invariance of the models, and derive the linearized fourth-order equation of motion for the metric, which describes massless and massive modes of propagation. In the limit of a large graviton mass, MCG reduces to general relativity (GR), whereas CG does not. Coordinates are fixed by Teyssandier gauge to show that for a conserved energy-momentum tensor the gravitational radiation is due to the time-dependent quadrupole moment of a non-relativistic source and we derive the gravitational energy-momentum tensor for both models. We apply our findings to the case of close binaries on circular orbits, which have been used to indirectly infer the existence of gravitational radiation prior to the direct observation of gravitational waves. As an example, we analyze the binary system PSR J1012+5307, chosen for its small eccentricity. When fixing the graviton mass in CG such that observed galaxy rotation curves could be explained without dark matter, the gravitational radiation of a binary system is much smaller than in GR. The same holds for MCG for small masses of the graviton. Thus gravitational radiation cannot explain the orbital decay of binary systems and replace dark matter simultaneously. We also analyse MCG for large graviton masses and conclude that MCG can describe the orbital periods of compact binaries in agreement with data, as it reduces to GR in that limit.