Cosmic time slip: Testing gravity on supergalactic scales with strong-lensing time delays

Abstract

We devise a test of nonlinear departures from general relativity (GR) using time delays in strong gravitational lenses. We use a phenomenological model of gravitational screening as a step discontinuity in the measure of curvature per unit mass, at a radius $\Lambda$. The resulting slip between two scalar gravitational potentials leads to a shift in the apparent positions and time delays of lensed sources, relative to the GR predictions, of size $\gamma_{\rm PN}-1$. As a proof of principle, we use measurements of two lenses, RXJ1121-1231 and B1608+656, to constrain deviations from GR to be below $|\gamma_{\rm PN}-1| \leq 0.2 \times (\Lambda/100\, \rm kpc)$. These constraints are complementary to other current probes, and are the tightest in the range $\Lambda=10-200$ kpc, showing that future measurements of strong-lensing time delays have great promise to seek departures from general relativity on kpc-Mpc scales.