Adiabatic regularization of functional determinants in cosmology and radiative corrections during inflation

TL;DR

This paper develops a method to regularize and renormalize the one-loop effective potential in cosmological spacetimes using adiabatic regularization, and applies it to inflationary models to analyze quantum corrections and their observational effects.

Contribution

It introduces a novel adiabatic regularization approach for functional determinants in cosmology, enabling the calculation of quantum corrections to inflationary potentials and curvature perturbations.

Findings

Radiative corrections to inflaton potentials are small but present after horizon crossing.

The method isolates effects of cosmic expansion in quantum corrections.

Effective potential for superhorizon curvature perturbation fects its scatterings with subhorizon modes.

Abstract

We express the in-in functional determinant giving the one-loop effective potential for a scalar field propagating in a cosmological spacetime in terms of the mode functions specifying the vacuum of the theory and then apply adiabatic regularization to make this bare potential finite. In this setup, the adiabatic regularization offers a particular renormalization prescription that isolates the effects of the cosmic expansion. We apply our findings to determine the radiative corrections to the classical inflaton potentials in scalar field inflationary models and also we derive an effective potential for the superhorizon curvature perturbation \zeta\ encoding its scatterings with the subhorizon modes. Although the resulting modifications to the cosmological observables like nongaussianity turn out to be small, they distinctively appear after horizon crossing.