Cancellation of one-loop time dependence in superhorizon curvature perturbations from all scales

Abstract

We show the conservation of the superhorizon curvature perturbations at one-loop level in spatially-flat gauge, including contributions from loop wavenumbers on all scales. In contrast to previous works, we do not assume a hierarchy $k \gg q$ between the wavenumber of the loop integral, $k$, and that of the power spectrum, $q$, and we explicitly include the regime $k \lesssim q$. Taking into account the nonlinear relation between the inflaton fluctuation and the curvature perturbation with the $δN$ formalism, we show that the apparent time dependence of the one-loop curvature power spectrum cancels once all contributions, including boundary terms, are combined consistently.