Probing Gravitational Slip with Strongly Lensed Fast Radio Bursts

The rapid accumulation of observed Fast Radio Bursts (FRBs) originating from cosmological distances makes it likely that some will be strongly lensed by intervening matter along the line of sight. Detection of lensed FRB repeaters, which account for a noteworthy fraction of the total population, will allow not only an accurate measurement of the lensing time delay, but also follow-up high-resolution observations to pinpoint the location of the lensed images. Recent works proposed to use such strongly-lensed FRBs to derive constraints on the current expansion rate $H_{0}$ as well as on cosmic curvature. Here we study the prospects for placing constraints on departures from general relativity via such systems. Using an ensemble of simulated events, we focus on the gravitational slip parameter $\gamma_{\rm PN}$ in screened modified gravity models and show that FRB time-delay measurements can yield constraints as tight as $\left| \gamma_{\rm PN}-1\right| \lesssim 0.04\times(\Lambda/100\rm kpc)\times[N/10]^{-1/2}$ at $1\sigma$ with $10$ detections.