Bispectrum at 1-loop in the Effective Field Theory of Inflation

TL;DR

This paper calculates 1-loop corrections to the bispectrum in the Effective Field Theory of Inflation, revealing the structure of divergences and the necessity of renormalization to remove unphysical logarithms.

Contribution

It introduces a method for computing 1-loop bispectrum corrections in EFToI using dimensional regularization and analyzes the structure of divergences and their cancellation.

Findings

1-loop bispectrum corrections involve logarithmic structures.

Unrenormalised results contain unphysical momentum logarithms.

Renormalisation removes unphysical divergences.

Abstract

In this paper we compute 1-loop corrections to the bispectrum in the decoupling limit of the Effective Field Theory of Inflation (EFToI). We regulate the divergences by employing dimensional regularization and work in $d=3+\delta$ dimensions. We find that the final results feature analytic structures of the form $\log{\left(k_i/k_T\right)}$ and $\log{\left(H/\mu\right)}$, where $H$ is the Hubble parameter and $\mu$ is the renormalisation scale. An interesting outcome of our calculations is that unlike the 1-loop correction to the power-spectrum computed in arXiv:0912.2734 the unrenormalised answers always produce unphysical logarithms of co-moving momenta. These unphysical logarithms are cancelled only after renormalisation. We expect this to be a generic feature for loop computations unless there is some cancellation as in the previously computed 1-loop result for the power-spectrum.