On Adiabatic Renormalization with a Physically Motivated Infrared Cut-Off

TL;DR

This paper proposes a new adiabatic renormalization method in curved space-time using a physically motivated infrared cut-off to avoid unphysical divergences, demonstrated through an inflationary model with gauge fields.

Contribution

It introduces an infrared cut-off in adiabatic subtraction, providing a well-defined renormalization scheme in curved space-time.

Findings

Infrared cut-off prevents unphysical divergences.

Method correctly reproduces the conformal anomaly.

Applicable to inflationary models with gauge fields.

Abstract

We introduce a new approach to renormalize physical quantities in curved space-time by adiabatic subtraction. We use a comoving infrared cut-off in defining the adiabatic counterpart of the physical quantity under consideration, building on the fact that the adiabatic approximation is ill-defined in the infrared tail of the spectrum. We show how this infrared cut-off should be used to obtain a completely well-defined renormalization scheme and how it is fundamental to avoid unphysical divergences that can be generated by a pathological behavior of the adiabatic subtraction extended to the infrared tail. The infrared cut-off appears as a new degree of freedom introduced in the theory and its actual value has to be consistently fixed by a physical prescription. As an example, we show how such degree of freedom can be set to obtain the correct value of the conformal anomaly in the symptomatic case of an inflationary model with gauge fields coupled to a pseudo-scalar inflaton.