Reconstructing f (R) gravity from the spectral index

Abstract

Recent cosmological observations are in good agreement with the scalar spectral index ns with ns − 1 −2/N, where N is the number of e-foldings. In previous work [T. Chiba, Prog. Theor. Exp. Phys. 2015, 073E02 (2015)], the reconstruction of the inflaton potential for a given ns was studied, and it was found that, for ns − 1 = −2/N, the potential takes the form of either an α-attractor model or a chaotic inflation model with φ2 to the leading order in the slow-roll approximation. Here we consider the reconstruction of the f (R) gravity model for a given ns both in the Einstein frame and in the Jordan frame. We find that for ns − 1 = −2/N (or more general ns − 1 = −p/N), f (R) is given parametrically and is found to asymptote to R2 for large R. This behavior is generic as long as the scalar potential is of slow-roll type.