Dimensional Regularization of Bubble Diagrams in de Sitter Spacetime

TL;DR

The paper develops a dimensional-regularization framework for bubble diagrams in de Sitter spacetime using the Källén-Lehmann spectral representation to analytically compute 1-loop inflationary correlators with massive bulk propagators. The seed integral is decomposed into nonlocal, local, and background pieces and regulated by subtracting divergences via Riemann zeta-function techniques, implemented through MS subtraction. Applications include 1-loop 2-point and 1-loop 4-point functions in derivative-coupled scalar and massive vector models, with explicit counterterms whose coefficients depend on the Hubble parameter, revealing curvature couplings. The approach yields finite, renormalized results and aligns with flat-space limits, while offering a path to extend to more intricate loop topologies and fermionic cases, bolstering the theoretical toolkit for cosmological collider signals in inflationary cosmology.

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, Källén-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.

Figures (2)

• Figure 1: Feynman diagram of 1-loop 4-point correlator with a scalar loop.
• Figure 2: Feynman diagram of 1-loop 2-point correlator with a scalar loop.