CFHTLenS: testing the laws of gravity with tomographic weak lensing and redshift-space distortions

Dark energy may be the first sign of new fundamental physics in the Universe, taking either a physical form or revealing a correction to Einsteinian gravity. Weak gravitational lensing and galaxy peculiar velocities provide complementary probes of general relativity, and in combination allow us to test modified theories of gravity in a unique way. We perform such an analysis by combining measurements of cosmic shear tomography from the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) with the growth of structure from the WiggleZ Dark Energy Survey and the Six-degree-Field Galaxy Survey, producing the strongest existing joint constraints on the metric potentials that describe general theories of gravity. For scale-independent modifications to the metric potentials which evolve linearly with the effective dark energy density, we find present-day cosmological deviations in the Newtonian potential and curvature potential from the prediction of general relativity to be ΔΨ/Ψ = 0.05 ± 0.25 and ΔΦ/Φ = −0.05 ± 0.3, respectively (68 per cent confidence limits).