A polynomial f(R) inflation model

Abstract

Motivated by the ultraviolet complete theory of quantum gravity, for example the string theory, we investigate a polynomial f(R) inflation model in detail. We calculate the spectral index and tensor-to-scalar ratio in the f(R) inflation model with the form of F(R)=R + R2/6M2+λ n/2n Rn/(3M2)n-1. Compared to Planck 2013, we find that Rn term should be exponentially suppressed, i.e. |λn|10-2n+2.6.