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 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 ∼eq {-}8 × 10^{-4} for a quartic potential. For a general monomial potential, α is constrained in the range -2.7× 10^{-3} < α < -6 × 10^{-4} as long as |ξ |≤ 10^{-3} if r< 0.1.