On counterterms in cosmological perturbation theory

TL;DR

This paper investigates the renormalization process in cosmological perturbation theory, revealing that late-time limits erase information about counter terms, contrasting with standard quantum field theory expectations.

Contribution

It highlights a unique aspect of renormalization in cosmological perturbation theory, showing how counter term information is lost at late times, unlike in conventional quantum field theories.

Findings

Late-time limits erase counter term information

Renormalization of curvature perturbation field strength discussed

Contrasts with standard QFT renormalization processes

Abstract

Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counter terms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counter terms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counter terms shall be needed to renormalize the theory than are actually required. We also comment on how the field strength of curvature perturbation, $\zeta$, could get renormalized.