Second-order weak lensing from modified gravity

We explore the sensitivity of weak gravitational lensing to second-order corrections to the spacetime metric within a cosmological adaptation of the parametrized post-Newtonian framework. Whereas one might expect nonlinearities of the gravitational field to introduce non-Gaussianity into the statistics of the lensing convergence field, we show that such corrections are actually always small within a broad class of scalar-tensor theories of gravity. We show this by first computing the weak lensing convergence within our parametrized framework to second order in the gravitational potential, and then computing the relevant post-Newtonian parameters for scalar-tensor gravity theories. In doing so we show that this potential systematic factor is generically negligible, thus clearing the way for weak lensing to provide a direct tracer of mass on cosmological scales for a wide class of gravity theories despite uncertainties in the precise nature of the departures from general relativity.

Figure 1

A sketch of our setup. The observer is a comoving distance $w$ away from the source, $\theta$ is the angular coordinate on the sky, $\widehat{\alpha }$ is the deflection angle felt by the ray, and $\alpha$ is the angular change in sky position as seen by the observer.