Confirmation of general relativity on large scales from weak lensing and galaxy velocities

Abstract

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed¹, using a quantity, E_G, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to ‘galaxy bias’ (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of E_G different from the general relativistic prediction because, in these theories, the ‘gravitational slip’ (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure² and the strength of the gravitational lensing effect³. Here we report that E_G = 0.39 ± 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of E_G ≈ 0.4. The measured value excludes a model¹ within the tensor–vector–scalar gravity theory^4,5, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f() theory⁶, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.