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 ${\gamma }_{\mathrm{PN}}-1$. As a proof of principle, we use measurements of two lenses, RXJ1121-1231 and B1608+656, to constrain deviations from GR to be below $|{\gamma }_{\mathrm{PN}}-1|\le 0.2\times (\Lambda /100\mathrm{kpc})$. 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.

9 pages, 3 figures. Expanded discussion. Published in Phys Rev D