Testing gravity with non-Gaussianity

Abstract

We show that modified gravity presents distinctive nonlinear features on the Cosmic Microwave Background (CMB) anisotropies comparing with General Relativity (GR). We calculate the contribution to the CMB non-Gaussianity from nonlinear Sachs-Wolfe effect in $f(R)$ gravity and show that, contrary to GR's contribution which is typically $\lesssim \mathcal{O}(1)$, the contribution in $f(R)$ gravity is sensitive to the nonlinear structure of $f(R)$ and can be large in principle. Optimistically, this gives an alternative origin for the possibly observed large CMB non-Gaussianities besides the primordial ones. On the other hand, such nonlinear features can be employed to provide a new cosmological test of $f(R)$ or other modified theories of gravitation, which is unique and independent of previously known tests.