Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

TL;DR

This paper develops a parametrized model for Lorentz-violating modifications to gravitational wave dispersion relations, analyzing their effects on wave propagation and how gravitational wave observations can constrain such violations.

Contribution

It introduces a flexible dispersion relation framework for Lorentz violation in gravity and connects it to gravitational wave waveform analysis for testing fundamental physics.

Findings

Constraints are tightest for small power dispersion relations.

Modified dispersion affects phase evolution detectable by gravitational wave observatories.

No evidence of Lorentz violation found within current observational limits.

Abstract

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.