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

TL;DR

This paper provides a general framework to estimate how trans-Planckian physics could modify the primordial power spectrum during inflation, highlighting the dependence on boundary conditions at a cutoff scale.

Contribution

It introduces a universal expression for scalar and tensor power spectra considering arbitrary boundary conditions at a short-distance cutoff during inflation.

Findings

Modulation of power spectra is of order H/M at the cutoff scale.

Shape of the modulation depends on deviation from de Sitter spacetime.

The behavior is generic but not unavoidable.

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 $p = M$, we find that the modulation to the power spectra of density and gravitational wave fluctuations is of order $(H/M)$, where $H$ is the Hubble parameter during inflation, and we argue that this behavior is generic, although by no means inevitable. With 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.