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

11 pages, 4 figures, to appear in PTEP