Generic estimate of trans-Planckian modifications to the primordial power spectrum in inflation

Abstract

We derive a general expression for the power spectra of scalar and tensor fluctuations generated during inflation given an arbitrary choice of boundary condition for the mode function at a short distance. We assume that the boundary condition is specified at a short-distance cutoff at a scale M which is independent of time. Using a particular prescription for the boundary condition at momentum $p\sim M,$ we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $\mathrm{}(H/M),$ where H is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With a fixed boundary condition, we find that the shape of the modulation to the power spectra is determined entirely by the deviation of the background spacetime from the de Sitter limit.