On Cosmological Correlators at One Loop

TL;DR

This paper analyzes one-loop equal-time correlators of massless scalar fields in flat space, revealing their simpler structure compared to wavefunction coefficients, and introduces methods to evaluate and classify their singularities.

Contribution

It introduces a systematic approach using a cosmological analogue of the Baikov representation to evaluate one-loop correlators and classifies their singularities with Landau analysis.

Findings

Bubble diagram has a UV divergence removable by a counterterm.

Triangle diagram yields a finite result expressed with dilogarithms.

Derived a factorization property relating cosmological correlators to flat-space amplitudes.

Abstract

We study equal-time in-in correlators of massless scalar fields in flat space at one loop. Using the time-ordered decomposition of correlators together with a cosmological analogue of the Baikov representation, we systematically construct relatively simple loop integrals and make manifest why, in this setting, loop corrections to correlators are simpler than those of wavefunction coefficients. As benchmark examples, we analyse the bubble and triangle diagrams. The bubble exhibits a UV divergence that can be removed by a local counterterm, while the triangle yields a finite result, which we evaluate explicitly in terms of dilogarithms using an integral transform for the Laplacian Green's function. We classify the kinematic singularities of these diagrams using Landau analysis, identifying novel types of singular behaviour, and validate this analysis against the explicit results. Finally, we derive a factorisation property of one-loop cosmological correlators at singular kinematics, relating them to flat-space loop amplitudes and lower-point tree-level correlators.