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 f (R) = R +R-2/6M(2) + lambda n/2n R-n/(3M(2))(n - 1). Compared to Planck 2013, we find that R-n term should be exponentially suppressedn, i.e. vertical bar lambda(n)vertical bar less than or similar to 10(-2n+2.6).