No evidence for modifications of gravity from galaxy motions on cosmological scales

Current tests of general relativity (GR) remain confined to the scale of stellar systems or the strong gravity regime. A departure from GR on cosmological scales has been advocated1 as an alternative to the cosmological constant Λ (ref. 2) to account for the observed cosmic expansion history3,4. However, such models yield distinct values for the linear growth rate of density perturbations and consequently for the associated galaxy peculiar velocity field. Measurements of the resulting anisotropy of galaxy clustering5,6 have thus been proposed as a powerful probe of the validity of GR on cosmological scales7, but despite substantial efforts8,9, they suffer from systematic errors comparable to statistical uncertainties10. Here, we present the results of a forward-modelling approach that fully exploits the sensitivity of the galaxy velocity field to modifications of GR. We use state-of-the-art high-resolution N-body simulations of a standard GR (Λ cold dark matter (CDM)) model11 and a compelling f(R) model12—one of GR’s simplest variants, in which the Ricci scalar curvature, R, in the Einstein–Hilbert action is replaced by an arbitrary function of R—to build simulated catalogues of stellar-mass-selected galaxies through a robust match to the Sloan Digital Sky Survey13. We find that f(R) fails to reproduce the observed redshift-space clustering on scales of ~1–10 Mpc h−1, where h is the dimensionless Hubble parameter. Instead, the standard ΛCDM GR model agrees impressively well with the data. This result provides strong confirmation, on cosmological scales, of the robustness of Einstein’s general theory of relativity.