Cosmological UV/IR Divergences and de-Sitter Spacetime

TL;DR

This paper investigates one-loop graviton corrections to scalar Green's functions in de Sitter space, emphasizing the importance of UV and IR cutoff choices and demonstrating consistent results across multiple regularization schemes.

Contribution

It introduces a consistent framework for implementing UV and IR cutoffs in de Sitter space and compares three regularization schemes, showing they yield the same physical results.

Findings

All three regularization schemes produce the same scalar propagator results.

The UV cutoff should be fixed in physical coordinates, while the IR cutoff expands with space.

Regularization schemes are interchangeable when properly implemented.

Abstract

We consider one loop graviton corrections to scalar field Green's functions in the de Sitter phase of an inflationary space-time, a topic relevant to the computation of cosmological observables beyond linear order. By embedding de-Sitter space into an ultraviolet complete theory such as M-theory we argue that the ultraviolet (UV) cutoff of the effective field theory should be taken to be fixed in physical coordinates, whereas the infrared (IR) cutoff is expanding as space expands. In this context, we demonstrate how to implement three different regularization schemes -- the brute force cutoff regularization, dimensional regularization and Pauli-Villars regularization -- obtaining the same result for the scalar propagator if we use any of the three regularization schemes.