Consistency Relations for Large Field Inflation: Non-minimal Coupling

Abstract

We derive the consistency relations for a chaotic inflation model with a non-minimal coupling to gravity. For a quadratic potential in the limit of a small non-minimal coupling parameter $\xi$ and for a quartic potential without assuming small $\xi$, we give the consistency relations among the spectral index $n_s$, the tensor-to-scalar ratio $r$ and the running of the spectral index $\alpha$. We find that unlike $r$, $\alpha$ is less sensitive to $\xi$. If $r<0.1$, then $\xi$ is constrained to $\xi<0$ and $\alpha$ is predicted to be $\alpha\simeq -8\times 10^{-4}$ for a quartic potential. For a general monomial potential, $\alpha$ is constrained in the range $-2.7\times 10^{-3}<\alpha< -6\times 10^{-4}$ as long as $|\xi|\leq 10^{-3}$ if $r<0.1$.