Consistency Relations for Large Field Inflation: Non-minimal Coupling

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 $alphasimeq -8times 10^{-4}$ for a quartic potential. For a general monomial potential, $alpha$ is constrained in the range $-2.7times 10^{-3}<alpha< -6times 10^{-4}$ as long as $|xi|leq 10^{-3}$ if $r<0.1$.