The Impact of Ultraviolet Regularization on the Spectrum of Curvature Perturbations During Inflation

TL;DR

This paper examines how ultraviolet regularization affects the spectrum of curvature perturbations during inflation, arguing that leading-order predictions do not require regularization, and critiques traditional adiabatic subtraction methods.

Contribution

It clarifies the role of regularization in inflationary predictions and highlights issues with traditional adiabatic subtraction techniques.

Findings

Two-point function is finite at leading order without regularization.

Regularization is necessary only for non-linear corrections.

Traditional adiabatic subtraction introduces undesirable features.

Abstract

Inflationary predictions based on the linear theory of cosmological perturbations are related to the two point function of a (second quantized) real scalar free field during the accelerated stage. Such a two point function is finite, in contrast with its coincidence limit, which is divergent due to the ultraviolet divergences proper of field theory. We therefore argue that predictions of most of the inflationary models do not necessarily need a regularization scheme to leading order, i.e. tree level, which is required instead for non-linear corrections or calculations involving the energy-momentum tensor. We also discuss unpleasant features of the "would be" regularized spectrum obtained using the traditional fourth order adiabatic subtraction.