Testing Gravity Against Early Time Integrated Sachs-Wolfe Effect

Abstract

A generic prediction of general relativity is that the cosmological linear density growth factor $D$ is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent $D$ 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 $f(R)$ gravity, with the form $f(R)=-{\lambda }_1{H}_0^2\exp (-R/{\lambda }_2{H}_0^2)$. Such $f(R)$ gravity, even with degenerate expansion history to $\Lambda$CDM, can produce detectable ISW effect at $z\ga 3$ and $l\ga 20$. Null-detection of such effect would constrain ${\lambda }_2$ to be ${\lambda }_2>1000$ at $>95$ confidence level. On the other hand, robust detection of ISW-LSS cross correlation at high $z$ will severely challenge general relativity.

5 pages, 2 figures. Accepted to PRD. v2: Revised to address to more general audience. v3: added discussions

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