Testing general relativity with gravitational waves: Improving and extending modified dispersion relation tests

Searching for a modified dispersion relation is one of the general relativity tests performed by the LIGO-Virgo-KAGRA Collaboration with each new cumulative Gravitational Wave Transient Catalog (GWTC). It considers classes of theories that modify the dispersion of gravitational waves by introducing a massive graviton or breaking Lorentz invariance. The symmetry breaking is parameterized phenomenologically by a momentum power law term p α added to the dispersion relation, with the test placing constraints on the amplitude A α of the introduced deviation. In this work, we implement improvements to the test, chief among them group velocity parameterization, a better sampling procedure, and extension to negative exponents α of p . We then reanalyze the events from the third catalog, GWTC-3, with our improved method. Compared with GWTC-3 results, the individual event posteriors have significantly higher effective sample size and fewer multimodalities. The combined posteriors on the amplitude parameters A α are, on average, 19% narrower. The 90% upper bound on the graviton mass changes from 2.42 × 10 − 11 to 2.21 × 10 − 11 peV . For the extension of our test to α ∈ { − 1 , − 2 , − 3 } , we find no evidence in favor of general relativity violation.