Testing the variation of the fine structure constant with strongly lensed gravitational waves

TL;DR

This paper proposes a method using strongly lensed gravitational waves and electromagnetic signals to test potential variations in the fine structure constant across cosmological distances, providing new bounds and insights into alternative gravity theories.

Contribution

It introduces a novel approach to constrain the variation of the fine structure constant using time delay differences in lensed gravitational wave and electromagnetic signals.

Findings

Upper bound on dipolar amplitude: $B\cos\theta \leq 1.85\times10^{-5}$

Results are consistent with current observational limits on $\alpha_e$

Method can distinguish between different theories of gravity explaining $\alpha_e$ variation

Abstract

The possible variation of the electromagnetic fine structure constant $\alpha_e$ on cosmological scales arouses great interests in recent years. The strongly lensed gravitational waves and the electromagnetic counterparts could be used to test this variation. Under the assumption that the speed of photon could be modified, while the speed of GW is the same as GR predicated, and they both propagate in a flat Friedman-Robertson-Walker universe, we investigate the difference of time delays of the images and derive the upper bound of the variation of $\alpha_e$. For a typical lensing system in the standard cosmological models, we obtain $B\cos\theta\leq 1.85\times10^{-5}$, where $B$ is the dipolar amplitude and $\theta$ is the angle between observation and the preferred direction. Our result is consistent with the most up-to-date observations on $\alpha_e$. In addition, the observations of strongly lensed gravitational waves and the electromagnetic counterparts could be used to test which types of alternative theories of gravity can account for the variation of $\alpha_e$.