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

TL;DR

A test of the applicability of general relativity on cosmological length scales using a quantity that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate, reports that EG = 0.39 ± 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction.

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, EG, 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 EG 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 effect3. Here we report that EG = 0.39 +/- 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of EG $\approx$ 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.

Figures (2)

• Figure 1: | Probes of large-scale structure measured from$\boldsymbol{\sim} \mathbf{7 0 , 0 0 0}$
• Figure 2: | Comparison of observational constraints with predictions from$\mathbf{G R}$ and viable modified gravity theories. Estimates of $E_{G}(R)$ are shown with $1 \sigma$ error bars (s.d.) including the statistical error on the measurement ${ }^{19}$ of $\beta$ (filled circles). The grey shaded region indicates the $1 \sigma$ envelope of the mean $E_{G}$ over scales $R=10-50 h^{-1} \mathrm{Mpc}$, where the systematic effects are least important (see Supplementary Information). The horizontal line shows the mean prediction of the $\mathrm{GR}+\Lambda \mathrm{CDM}$ model, $E_{G}=\Omega_{\mathrm{m}, 0} / f$, for the effective redshift of the measurement, $z=0.32$. On the right side of the panel, labelled vertical bars show the predicted ranges from three different gravity theories: (i) $\mathrm{GR}+\Lambda \mathrm{CDM}$ ( $E_{G}=0.408 \pm 0.029(1 \sigma)$ ), (ii) a class of cosmologically-interesting models in $f(R)$ theory with Compton wavelength parameters ${ }^{27} B_{0}=0.001-0.1$ ( $E_{G}=0.328-0.365$ ), and (iii) a TeVeS model ${ }^{9}$ designed to match existing cosmological data and to produce a significant enhancement of the growth factor ( $E_{G}=0.22$, shown with a nominal error bar of 10 per cent for clarity).