On Adiabatic Renormalization of Inflationary Perturbations

TL;DR

This paper examines how adiabatic renormalization affects inflationary perturbation spectra, revealing ambiguities and questioning its validity at horizon exit, suggesting unrenormalized spectra are physically meaningful.

Contribution

It demonstrates the ambiguity of adiabatic regularization schemes and argues that unrenormalized spectra are the true physical quantities in the infrared regime.

Findings

Adiabatic regularization schemes yield different results in the infrared.

All schemes agree in the ultraviolet regime.

Unrenormalized spectra are physically meaningful in the infrared.

Abstract

We discuss the impact of adiabatic renormalization on the power spectrum of scalar and tensor perturbations from inflation. We show that adiabatic regularization is ambiguous as it leads to very different results, for different adiabatic subtraction schemes, both in the range $v\equiv k/(aH) \gsim 0.1$ and in the infrared regime. All these schemes agree in the far ultraviolet, $v\gg 1$. Therefore, we argue that in the far infrared regime, $v\ll 1$, the adiabatic expansion is no longer valid, and the unrenormalized spectra are the physical, measurable quantities. These findings cast some doubt on the validity of the adiabatic subtraction at horizon exit, $v=1$, to determine the perturbation spectra from inflation which has recently advocated in the literature.