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 $f(R)=R+\frac{R^2}{6M^2}+\frac{{\lambda }_n}{2n}\frac{R^n}{(3M^2{)}^{n-1}}$. Compared to Planck 2013, we find that $R^n$ term should be exponentially suppressed, i.e. $|{\lambda }_n|\lesssim 10^{-2n+2.6}$.

Comments: 5 pages, 3 figures; refs added, version accepted for publication in JCAP