A polynomial f(R) inflation model

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 . Compared to Planck 2013, we find that R n term should be exponentially suppressed, i.e. |λ n |≲10 −2 n +2.6 .