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, 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 structure2 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 ≈ 0.4. The measured value excludes a model1 within the tensor–vector–scalar gravity theory4,5, 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.
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Zhang, P., Liguori, M., Bean, R. & Dodelson, S. Probing gravity at cosmological scales by measurements which test the relationship between gravitational lensing and matter overdensity. Phys. Rev. Lett. 99, 141302 (2007)
Daniel, S. F., Caldwell, R. R., Cooray, A., Serra, P. & Melchiorri, A. Multiparameter investigation of gravitational slip. Phys. Rev. D 80, 023532 (2009)
Uzan, J. P. & Bernardeau, F. Lensing at cosmological scales: a test of higher dimensional gravity. Phys. Rev. D 64, 083004 (2001)
Milgrom, M. A modification of the Newtonian dynamics—implications for galaxies. Astrophys. J. 270, 371–389 (1983)
Bekenstein, J. D. Relativistic gravitation theory for the modified Newtonian dynamics paradigm. Phys. Rev. D 70, 083509 (2004)
Carroll, S. et al. Is cosmic speed-up due to new gravitational physics? Phys. Rev. D 70, 083509 (2004)
Hamilton, A. J. S. in The Evolving Universe (ed. Hamilton, D.) 185–275 (Astrophys. Space Sci. Library 231, Kluwer, 1998)
Baldauf, T., Smith, R. E., Seljak, U. & Mandelbaum, R. An algorithm for the direct reconstruction of the dark matter correlation function from weak lensing and galaxy clustering. Phys. Rev. D (submitted)
Bartelmann, M. & Schneider, P. Weak gravitational lensing. Phys. Rep. 340, 291–472 (2001)
Guzzo, L. et al. A test of the nature of cosmic acceleration using galaxy redshift distortions. Nature 451, 541–544 (2008)
Eisenstein, D. et al. Spectroscopic target selection for the Sloan Digital Sky Survey: the luminous red galaxy sample. Astron. J. 122, 2267–2280 (2001)
York, D. G. et al. The Sloan Digital Sky Survey: technical summary. Astron. J. 120, 1579–1587 (2000)
Eisenstein, D. et al. Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies. Astrophys. J. 633, 560–574 (2005)
Tegmark, M. et al. Cosmological constraints from the SDSS luminous red galaxies. Phys. Rev. D 74, 123507 (2006)
Mandelbaum, R. et al. Systematic errors in weak lensing: application to SDSS galaxy-galaxy weak lensing. Mon. Not. R. Astron. Soc. 361, 1287–1322 (2005)
Landy, S. D. & Szalay, A. S. Bias and variance of angular correlation functions. Astrophys. J. 412, 64–71 (1993)
Smith, R. E. Covariance of cross-correlations: towards efficient measures for large-scale structure. Mon. Not. R. Astron. Soc. 400, 851–865 (2009)
Seljak, U. Analytic model for galaxy and dark matter clustering. Mon. Not. R. Astron. Soc. 318, 203–213 (2000)
Dunkley, J. et al. Five-year Wilkinson Microwave Anisotropy Probe observations: likelihoods and parameters from the WMAP data. Astrophys. J. Suppl. Ser. 180, 306–329 (2009)
Will, C. M. The confrontation between general relativity and experiment. Space Sci. Rev. 148, 60–71 (2009)
Song, Y.-S., Hu, W. & Sawicki, I. The large scale structure of f(R) gravity. Phys. Rev. D 75, 044004 (2007)
Ferreira, P. G. & Starkman, G. D. Einstein’s theory of gravity and the problem of missing mass. Science 326, 812–815 (2009)
R.M. was supported for the duration of this work by NASA through a Hubble Fellowship grant awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA. U.S. acknowledges the Swiss National Foundation. T.B. acknowledges support by a grant from the German National Academic Foundation during the initial phase of this project.
Author Contributions R.R., R.M., U.S. and J.E.G. worked on the observational analysis, with R.R. doing most of the computations. T.B. and R.E.S. worked on the numerical simulations, with T.B. calculating the correction factors. L.L. worked on the theoretical predictions for comparison with the observations.
The authors declare no competing financial interests.
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Reyes, R., Mandelbaum, R., Seljak, U. et al. Confirmation of general relativity on large scales from weak lensing and galaxy velocities. Nature 464, 256–258 (2010). https://doi.org/10.1038/nature08857
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