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

Understand

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.