Cosmological Correlators at the Loop Level

TL;DR

This paper develops a method using partial Mellin-Barnes representation to calculate and renormalize 1-loop cosmological correlators, revealing new signals from boost-breaking bubble processes.

Contribution

It introduces a novel application of PMB representation for loop-level cosmological correlators, including renormalization and new boost-breaking bubble results.

Findings

Validated cutting rules for correlators

Demonstrated UV divergence cancellation with counterterms

Provided new analytical results for boost-breaking bubble signals

Abstract

Cosmological correlators encode rich information about physics at the Hubble scale and may exhibit characteristic oscillatory signals due to the exchange of massive particles. Although many 1-loop processes, especially those that break de Sitter (dS) boosts, can generate significant leading signals for various particle models in cosmological collider physics, the precise results for these correlators or their full signals remain unknown due to the lack of symmetry. In this work, we apply the method of partial Mellin-Barnes (PMB) representation to the calculation of cosmological correlators at the loop level. As a first step, we use the PMB representation to calculate four-point cosmological correlators with bubble topology. We find that both the nonlocal and local signals arise from the factorized part, validating the cutting rules proposed in previous work, and are free from UV divergence. Furthermore, the UV divergence originates solely from the background piece and can be manifestly canceled by introducing the appropriate counterterm, similar to the procedure in flat spacetime. We also demonstrate how to renormalize the 1-loop correlators in Mellin space. After a consistency check with known results for the covariant case, we provide new analytical results for the signals generated from a nontrivial dS-boost-breaking bubble.