Regularization and conformal transformations of the power spectrum in general single field inflation

TL;DR

This paper investigates the regularization of the CMB power spectrum in various inflation models, extending adiabatic regularization techniques and demonstrating their frame independence.

Contribution

It extends adiabatic regularization to generic inflation models, including k-inflation and non-minimally coupled cases, and analyzes their late-time behavior.

Findings

Derived subtraction terms for k-inflation models.

Showed regularization is frame-independent.

Analyzed late-time development of subtraction terms.

Abstract

The regularization of the CMB power spectrum is an important issue of cosmology. Most approaches assume that there is no need to regularize the power spectrum, while Parker advocated the new regularization approach for the power spectrum in 2007: the adiabatic regularization, which was originally developed for particle creation in curved spacetime. This thesis focuses on this issue, especially concerning adiabatic subtraction terms. The subtraction terms for minimally coupled slow-roll inflation are well known. We extend the view to more generic inflation models, and derive the subtraction terms for k-inflation models. Via the method of Urakawa-Starobinsky, we consider the time development of the subtraction term at late times. We also consider the non-minimally coupled case, and show that the adiabatic regularization is independent of the frame: Jordan or Einstein frames.