Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation

TL;DR

This paper demonstrates that in nonminimally coupled single-field inflation with varying sound speed, the adiabatic regularization causes the power spectrum's correction to decay exponentially, validating the use of the unregularized spectrum in standard models.

Contribution

It extends adiabatic regularization to nonminimally coupled inflation with varying sound speed, showing the regularized spectrum converges to the bare spectrum during inflation.

Findings

Subtraction term decays exponentially with e-folds.

Regularized spectrum approaches the bare spectrum.

Supports standard calculations in generalized inflation models.

Abstract

We perform adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation with varying speed of sound. The subtraction is performed within the framework of earlier study by Urakawa and Starobinsky dealing with the canonical inflation. Inspired by Fakir and Unruh's model on nonminimally coupled chaotic inflation, we find upon imposing near scale-invariant condition, that the subtraction term exponentially decays with the number of $ e $-folds. As in the result for the canonical inflation, the regularized power spectrum tends to the "bare" power spectrum as the Universe expands during (and even after) inflation. This work justifies the use of the "bare" power spectrum in standard calculation in the most general context of slow-roll single-field inflation involving non-minimal coupling and varying speed of sound.