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[1003.2185] Confirmation of general relativity on large scales from weak lensing and galaxy velocities
Authors:Reinabelle Reyes, Rachel Mandelbaum, Uros Seljak, Tobias Baldauf, James E. Gunn, Lucas Lombriser, Robert E. Smith
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.
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Beth Reid

Joined: 03 Dec 2009
Posts: 5
Affiliation: ICC Barcelona

PostPosted: March 11 2010  Reply with quote

The authors introduce a new statistic which eliminates both galaxy bias and sigma8 through the combination of galaxy-galaxy clustering, galaxy-galaxy lensing, and a measurement of redshift space distortions from anisotropic galaxy clustering. The authors present new measurements of the first two, and rely on Tegmark et al. (2006) for a measurement of β from redshift space distortions.

It can be used as a test of GR (and to constrain models of modified gravity). The statistic is

E_G = \frac{1}{\beta} \frac{\Gamma_{gm}(R)}{\Gamma_{gg}(R)}

which in GR+ΛCDM is Ωm,o / f(z) = 0.408±0.029.

Their measurements are in agreement with N-body + HOD mock LRG catalogs, indicating that the measurement is robust to non-linearities.

They compare to the predictions of f(R) and TeVeS, which predict substantially different values than GR+ΛCDM. While the errors are still quite large, this should prove to be an extremely valuable statistic in the near future.
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Neal Dalal

Joined: 25 Sep 2004
Posts: 7
Affiliation: CITA

PostPosted: March 11 2010  Reply with quote

Yes, this paper looks very interesting! Are they basically measuring the equality of the two metric potentials Φ and Ψ, assuming linear bias?

How should I interpret the f(R) prediction? Presumably, outside the Compton wavelength gravity matches GR, and inside the Compton wavelength gravity is 4/3 stronger, so is their result an upper bound on the Compton wavelength? Or does the Chameleon mechanism become important on the scales of interest, ˜20 Mpc? Or am I thinking about this wrong?

It's also neat that their measurement constrains Omega_m pretty well, to about 15%.
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