Confirmation of general relativity on large scales from weak lensing and galaxy velocities (1003.2185v1)

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.

• The paper presents a novel approach by integrating weak lensing, galaxy clustering, and redshift distortions to robustly measure EG as 0.39 ± 0.06 at z = 0.32.
• The methodology mitigates uncertainties from galaxy bias and matter perturbations by combining three complementary observational probes.
• The results validate GR predictions up to 50h⁻¹ Mpc and challenge modified gravity theories within the ΛCDM framework.

Confirmation of General Relativity on Large Scales from Weak Lensing and Galaxy Velocities

The paper investigates the applicability of General Relativity (GR), particularly in the context of cosmological scales where the accelerated expansion of the universe is observed. The research explores whether GR, when combined with the standard cosmological model under the ΛCDM framework, holds on scales up to tens of megaparsecs. This paper uses the Sloan Digital Sky Survey (SDSS) data, employing over 70,000 luminous red galaxies (LRGs), a sample optimal for studying large-scale cosmic structures.

The core of the paper involves a novel methodology that combines galaxy-galaxy lensing, galaxy clustering, and galaxy redshift distortions into a probe of gravity denoted as $E_G$. This combination aims to mitigate uncertainties inherent in individual measures such as galaxy bias and the amplitude of matter perturbations. This more integrative approach provides a robust and model-independent assessment of GR on large scales, measuring $E_G = 0.39 \pm 0.06$ at a redshift $z = 0.32$, which aligns closely with the GR+ΛCDM prediction of $E_G = 0.408 \pm 0.029$.

The application of three distinct observational probes enhances the credibility of the findings. Galaxy-galaxy lensing assesses the deflection of light by mass, sensitive to both the Newtonian potential $\phi$ and curvature potential $\psi$. Galaxy clustering measures these density perturbations, specifically reliant on the Newtonian potential $\phi$. Lastly, galaxy velocities examine redshift distortions, revealing the growth rate of structures influenced by gravitational forces. The results demonstrate consistency with GR, suggesting no observable gravitational slip and affirming the equivalency of scalar potentials without anisotropic stress, a conclusion that challenges modified gravity theories.

The results, verified across scales up to $R = 50h^{-1}$ Mpc, and powered by advanced statistical treatments like jackknife resampling, are rigorous and minimize systematic errors. The correction factors from dark matter simulations further support the results. This examination of $E_G$ aligns with GR predictions and provides what is essentially a non-trivial evaluation of modified gravity theories, such as the tensor-vector-scalar framework (TeVeS) and $f(R)$ gravity. The constraint on $E_G$ challenges modified theories, as evidenced by the tentative exclusion of certain TeVeS predictions.

The implications of this work extend into the field of future cosmological surveys, which could further refine these measurements with more extensive datasets and finer control of systemic errors. The approach underscores a direction toward more sophisticated gravitational models, improving our understanding of the cosmic acceleration. As this paper asserts its standing proof-of-concept, the anticipation for follow-up studies is pivotal in helping demystify the expansive phenomena observed within our universe. The consolidation of multiple lines of inquiry into a single measure enriches both theoretical exploration and practical applications, signaling a sophisticated methodological advance in cosmological astrophysics.