Renormalization of the inflationary perturbations revisited

TL;DR

This paper revisits the renormalization process for inflationary perturbations on curved backgrounds, clarifying the role of adiabatic subtraction and showing how it can be viewed as a redefinition of fundamental parameters, ensuring consistent observable predictions.

Contribution

It provides a new perspective on adiabatic subtraction as a set of counter terms, linking it to traditional renormalization and demonstrating how to maintain unrenormalized predictions for inflationary spectra.

Findings

Adiabatic subtraction can be expressed as counter terms in renormalization.

Renormalization of inflationary spectra can be achieved via redefinition of cosmological constant and Planck mass.

Observable predictions remain unchanged after proper renormalization.

Abstract

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.