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 proposed, 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 structure and the strength of the gravitational lensing effect. 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) approximately 0.4. The measured value excludes a model within the tensor-vector-scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f(R) theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

Observational probes of cosmic acceleration

“…To reach high precision on cosmological scales, the most promising route is to test for consistency between growth measurements from redshift-space distortions, which respond to the non-relativistic potential Ψ, and growth measurements from weak lensing. Implementing an approach suggested by Zhang et al (2007), Reyes et al (2010) present a form of this test that draws on redshift-space distortion measurements of SDSS luminous red galaxies by Tegmark et al (2006) and galaxy-galaxy lensing measurements of the same population. The precision of the test in Reyes et al (2010) is only ∼ 30%, limited mainly by the redshift-space distortion measurement, but this is already enough to rule out some otherwise viable models.…”

“…Implementing an approach suggested by Zhang et al (2007), Reyes et al (2010) present a form of this test that draws on redshift-space distortion measurements of SDSS luminous red galaxies by Tegmark et al (2006) and galaxy-galaxy lensing measurements of the same population. The precision of the test in Reyes et al (2010) is only ∼ 30%, limited mainly by the redshift-space distortion measurement, but this is already enough to rule out some otherwise viable models. In the long term, this approach could well be pushed to the sub-percent level, with the limiting factors being the modeling uncertainty in redshift-space distortions and systematics in weak lensing calibration.…”

“…• Reyes et al (2010) tested GR by comparing the galaxy-mass correlation function, measured via weak lensing, to the galaxy-velocity correlation function, measured via redshift-space distortions. The SDSS luminous red galaxy sample was chosen due to its large volume.…”

Beyond the cosmological standard model

“…A recent measurement was performed in [995], comparing galaxy-velocity and galaxy-shear crosscorrelations from the SDSS. They estimated E G ≈ 0.4, consistent with its value in GR, given by .…”

“…This test is fairly unique to testing gravity, as it has little information to add in the dark energy framework. At least 108 three kinds of tests are available: the comparison of strong lensing with measured stellar velocity dispersions in the inner parts of elliptical galaxies [996], the virial masses of halos from weak lensing and dynamics [997], and the infall region that extends to ten or more times the virial radius [995]. The latter two tests are feasible only for massive clusters or using stacked measurements of large samples of galaxies binned in luminosity or another observable that serves as a proxy for halo mass.…”