Fixing the Renormalization of Inflationary Loops via Ward Identities

TL;DR

This paper derives Ward identities from gauge symmetries to constrain and resolve ambiguities in the renormalization of quantum loop corrections in inflationary cosmology.

Contribution

It introduces a symmetry-based framework using Ward identities to non-perturbatively control the infrared evolution of the power spectrum in inflation.

Findings

Ward identities impose model-independent constraints on renormalization.

The framework resolves discrepancies in one-loop corrections for ultra-slow-roll inflation.

Symmetry considerations guide the consistent renormalization process.

Abstract

Evaluating quantum loop corrections to curvature perturbations in non-attractor inflation presents theoretical ambiguities. A crucial aspect of this challenge lies in the unconstrained finite contributions in renormalization counterterms and regularization scheme dependence. In this work, we derive exact Ward identities via the path integral formalism based on the large gauge symmetry of the background-perturbation split. These identities are shown to impose strict, model-independent constraints on the renormalization procedure. Provided the ultraviolet completion respects this symmetry, the Ward identities non-perturbatively govern the infrared evolution of the power spectrum. This symmetry-based framework offers a systematic resolution to recent theoretical discrepancies concerning one-loop corrections in ultra-slow-roll inflation.