Probing lens-induced gravitational-wave birefringence as a test of general relativity

Theories beyond general relativity (GR) modify the propagation of gravitational waves (GWs). In some, inhomogeneities (aka, gravitational lenses) allow interactions between the metric and additional fields to cause lens-induced birefringence (LIB): a different speed of the two linear GW polarizations (thorn and x). Inhomogeneities then act as nonisotropic crystals, splitting the GW signal into two components whose relative time delay depends on the theory and lens parameters. Here we study the observational prospects for GW scrambling, i.e. when the time delay between both GW polarizations is smaller than the signal's duration and the waveform recorded by a detector is distorted. We analyze the latest LIGO-Virgo-KAGRA catalog, GWTC-3, and find no conclusive evidence for LIB. The highest log Bayes factor that we find in favor of LIB is 3.21 for GW190521, a particularly loud but short event. However, when accounting for false alarms due to (Gaussian) noise fluctuations, this evidence is below 1 sigma. The tightest constraint on the time delay is < 0.51 ms at 90% confidence level (CL) from GW200311_115853. From the nonobservation of GW scrambling, we constrain the optical depth for LIB, accounting for the chance of randomly distributed lenses (e.g. galaxies) along the line of sight. Our LIB constraints on a (quartic) scalar-tensor Horndeski theory are more stringent than Solar System tests for a wide parameter range and comparable to GW170817 in some limits. Interpreting GW190521 as an active galactic nucleus (AGN) binary (i.e. taking an AGN flare as a counterpart) allows even more stringent constraints. Our results demonstrate the potential and high sensitivity achievable by tests of GR, based on GW lensing.

Automated summary

The study investigates the observational prospects for gravitational wave scrambling and lens-induced birefringence. Analysing the latest catalog of gravitational wave events, GWTC-3, no conclusive evidence for lens-induced birefringence is found. The tightest constraint on the time delay is < 0.51 ms at 90% confidence level. The results demonstrate the potential and high sensitivity achievable by tests of general relativity based on gravitational wave lensing.