Dimensional Regularization of Bubble Diagrams in de Sitter Spacetime

TL;DR

This paper develops a method using Källén-Lehmann representation and dimensional regularization to analytically compute loop correlators in de Sitter spacetime, addressing ultraviolet divergences in inflationary cosmology.

Contribution

It introduces a novel approach combining Källén-Lehmann representation with dimensional regularization for loop correlator calculations in de Sitter space.

Findings

Successfully computed 4-point and 2-point correlators with bubble loops

Demonstrated regularization of divergences in loop correlators

Applied method to massive scalars and spin-1 bosons

Abstract

Correlators of large-scale fluctuations produced during cosmic inflation are major observables of inflationary cosmology. In cosmological collider physics, many interesting correlators are generated through loop processes. However, ultraviolet divergences often appear when computing the loop correlators, and a regularization is required. In this work, K\"all\'en-Lehmann representation and dimensional regularization are used to analytically compute various correlators with a bubble loop of massive bulk propagators in de Sitter spacetime. Examples include 4-point and 2-point correlators with 1-loop bubble exchanges of derivatively coupled massive scalars or massive spin-1 bosons.