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Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect

Abstract

A generic prediction of general relativity is that the cosmological linear density growth factor DD is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent DD can cause time variation in gravitational potential at high redshifts and provides a new cosmological test of gravity, through early time integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. We demonstrate the power of this test for a class of f(R)f(R) gravity, with the form f(R)=λ1H02exp(R/λ2H02)f(R)=-\lambda_1 H_0^2\exp(-R/\lambda_2H_0^2). Such f(R)f(R) gravity, even with degenerate expansion history to Λ\LambdaCDM, can produce detectable ISW effect at z\ga 3 and l\ga 20. Null-detection of such effect would constrain λ2\lambda_2 to be λ2>1000\lambda_2>1000 at >95>95% confidence level. On the other hand, robust detection of ISW-LSS cross correlation at high zz will severely challenge general relativity.Comment: 5 pages, 2 figures. Accepted to PRD. v2: Revised to address to more general audience. v3: added discussion

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