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 Delta Psi/Psi = 0.05 +/- 0.25 and Delta Phi/Phi = -0.05 +/- 0.3, respectively (68 per cent confidence limits).