Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes

TL;DR

This paper introduces a new regularization method for the scalar field power spectrum in cosmological spacetimes that reduces infrared distortions while maintaining ultraviolet divergence removal, improving upon adiabatic regularization.

Contribution

The authors propose a novel subtraction scheme based on renormalization ambiguities that minimizes infrared distortions in the power spectrum, compatible with local covariance and general regularization methods.

Findings

The new method reduces infrared distortions compared to adiabatic regularization.

In de Sitter space, the scheme recovers the standard scale-invariant power spectrum.

The approach is consistent with local covariance and general regularization principles.

Abstract

We reexamine the regularization of the two-point function of a scalar field in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic regularization provides a set of subtraction terms in momentum space that successfully remove its ultraviolet divergences at coincident points, but can significantly distort the power spectrum at infrared scales, especially for light fields. In this work we propose, by using the intrinsic ambiguities of the renormalization program, a new set of subtraction terms that minimize the distortions for scales $k \lesssim M$, with $M$ an arbitrary mass scale. Our method is consistent with local covariance and equivalent to general regularization methods in curved spacetime. We apply our results to the regularization of the power spectrum in de Sitter space: while the adiabatic scheme yields exactly $\Delta_{\phi}^{\rm (reg)} = 0$ for a massless field, our proposed prescription recovers the standard scale-invariant result $\Delta_{\phi}^{\rm (reg)} \simeq H^2 /(4\pi^2)$ at super-horizon scales.