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

TL;DR

This paper investigates the potential of gravitational-wave lensing-induced birefringence as a test of general relativity, analyzing LIGO-Virgo-KAGRA data to constrain alternative theories and find no conclusive evidence for birefringence effects.

Contribution

It introduces a method to test gravitational-wave birefringence caused by lensing, providing the first constraints from GW data and comparing them with other tests of gravity.

Findings

No conclusive evidence for lens-induced birefringence in GWTC-3 data.

The tightest time delay constraint is less than 0.51 ms at 90% confidence.

Constraints on scalar-tensor theories surpass some solar system tests.

Abstract

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 polarisations ($+$ and $\times$). Inhomogeneities then act as non-isotropic 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 polarisations 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 favour of LIB is $3.21$ for GW$190521$, 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 (90% C.L.) from GW$200311\_115853$. From the non-observation of GW scrambling, we constrain the optical depth for LIB, accounting for the chance of randomly distributed lenses (eg. 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 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.