On the renormalization of ultraviolet divergences in the inflationary angular power spectrum

TL;DR

This paper examines how ultraviolet divergences in quantum fields during inflation affect the angular power spectrum, proposing a refined renormalization approach that could alter theoretical predictions while preserving scale invariance.

Contribution

It introduces a space-time perspective for renormalizing cosmological observables and suggests higher-order adiabatic renormalization may be more suitable than standard methods.

Findings

Standard renormalization corresponds to zero adiabatic order.

Second-order adiabatic renormalization may significantly change $C_{\,ell}$ predictions.

Scale invariance of the power spectrum is maintained despite renormalization changes.

Abstract

We revise the role that ultraviolet divergences of quantum fields play in slow-roll inflation, and discuss the renormalization of cosmological observables from a space-time perspective, namely the angular power spectrum. We first derive an explicit expression for the multipole coefficients $C_{\ell}$ in the Sachs-Wolfe regime in terms of the two-point function of primordial perturbations. We then analyze the ultraviolet behavior, and point out that the standard result in the literature is equivalent to a renormalization of $C_{\ell}$ at zero ``adiabatic'' order. We further argue that renormalization at second ``adiabatic'' order may be more appropriate from the viewpoint of standard quantum field theory. This may change significantly the predictions for $C_{\ell}$, while maintaining scale invariance.