Finite parts of inflationary loops II: A streamlined UV in-in algorithm and distinguishable signatures

TL;DR

This paper presents a new streamlined method for evaluating in-in loop integrals in inflationary models, focusing on ultraviolet contributions and finite parts, with applications to the primordial bispectrum.

Contribution

The authors develop a simplified UV in-in algorithm that aids in extracting finite parts of loop corrections and identifying distinguishable signatures in inflationary correlators.

Findings

Introduced a streamlined UV in-in loop integral evaluation method.

Identified a difficulty in renormalization within the in-in formalism.

Applied the method to the one-loop primordial bispectrum, finding distinguishable signatures.

Abstract

We introduce a streamlined method for evaluating in-in loop integrals using dimensional regularization for diagrams with an arbitrary number of external legs and vertices, which complements earlier work and facilitates the extraction of the ultraviolet contributions. The method leads us to identify an apparent difficulty to renormalize with Hamiltonian counterterms within the in-in formalism. We also discuss the importance of the finite parts of loop corrections that can be distinguished from their associated counterterm contributions. As an application, we examine the one-loop primordial bispectrum in the context of the effective field theory of inflation, considering a specific set of interactions, and identifying a contribution distinguishable from its tree-level counterpart.