Effective speed of gravitational waves

Abstract

We derive an effective equation and action for the propagation of gravitational waves (GW), encoding the effects of interaction and self-interaction in a time, frequency and polarization dependent effective speed. In terms of an appropriately defined effective metric, the effective action takes the form a massless Klein-Gordon action. This effective approach predicts that for theories with matter coupled to the Einstein frame metric the ratio between gravitational and electromagnetic (EM) luminosity distance depends on the effective speed, while for Jordan frame matter coupling it depends on the effective Planck mass. We discuss how the frequency and polarization dependence of the GW-EM distance ratio provides a new test of general relativity and its modifications, and more in general of the interaction of GWs with other fields.

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• A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events
• Constraining the effective field theory of dark energy with multimessenger astronomy
• Measuring the speed of gravity and the cosmic expansion with time delays between gravity and light from binary neutron stars
• Effective speed of cosmological perturbations