The Trispectrum in the Effective Field Theory of Large Scale Structure

TL;DR

This paper calculates the four-point correlation function (trispectrum) of cosmological density perturbations at one-loop order using Standard Perturbation Theory and the Effective Field Theory of Large Scale Structure, clarifying EFT subtleties.

Contribution

It introduces a comprehensive calculation of the EFT trispectrum, including vorticity and non-locality, for various configurations relevant to primordial non-Gaussianity constraints.

Findings

EFT contributions to the trispectrum are explicitly computed.

Vorticity and non-locality are incorporated into EFT counterterms.

Predictions for configurations relevant to primordial non-Gaussianity are provided.

Abstract

We compute the connected four point correlation function (the trispectrum in Fourier space) of cosmological density perturbations at one-loop order in Standard Perturbation Theory (SPT) and the Effective Field Theory of Large Scale Structure (EFT of LSS). This paper is a companion to our earlier work on the non-Gaussian covariance of the matter power spectrum, which corresponds to a particular wavenumber configuration of the trispectrum. In the present calculation, we highlight and clarify some of the subtle aspects of the EFT framework that arise at third order in perturbation theory for general wavenumber configurations of the trispectrum. We consistently incorporate vorticity and non-locality in time into the EFT counterterms and lay out a complete basis of building blocks for the stress tensor. We show predictions for the one-loop SPT trispectrum and the EFT contributions, focusing on configurations which have particular relevance for using LSS to constrain primordial non-Gaussianity.