Ultraviolet Divergences in Cosmological Correlations

TL;DR

This paper introduces a novel method to handle ultraviolet divergences in cosmological correlation calculations without relying on dimensional regularization, using an extended WKB approximation and Pauli-Villars regulators.

Contribution

It develops a regulator-independent approach for ultraviolet divergence control in cosmological correlations, providing explicit formulas and prescriptions for finite calculations.

Findings

Successfully cancels all regulator dependence in correlation functions

Provides explicit formulas for counterterms

Addresses potential infrared divergences

Abstract

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite regulator-independent correlation functions. The possibility of infrared divergences in this theory is briefly considered.