Precise Calibration of the One-Loop Trispectrum in the Effective Field Theory of Large Scale Structure

TL;DR

This paper calibrates the effective field theory counterterms for the one-loop trispectrum in large-scale structure, demonstrating their necessity and consistency across different n-point functions, and highlighting errors from common approximations.

Contribution

It provides the first explicit calibration of EFT counterterms for the one-loop trispectrum, establishing their non-zero nature and consistency with lower-order functions.

Findings

EFT counterterms are necessary for accurate trispectrum modeling.

Two one-parameter ansätze effectively correct residuals below k~0.07 h/Mpc.

Using bispectrum-derived amplitudes ensures consistency across n-point functions.

Abstract

The Large-Scale Structure (LSS) of the universe has the potential to provide decisive answers to the remaining open questions in cosmology. Early attempts at modelling it analytically focused on using perturbation theory. However, small-scale effects introduced by gravitational collapse cannot be described perturbatively and this failure of perturbation theory is reflected even on the largest scales. The Effective Field Theory of Large Scale Structure (EFTofLSS) has emerged as a consistent method for describing LSS on large scales by introducing counterterms that account for the effects of small-scale dynamics. So far studies of the EFT have mostly focused on the two and three point functions with little attention devoted to the four point function or trispectrum. The trispectrum probes cubic interactions arising from non-linear clustering, biasing, and primordial non-Gaussianities, and constitutes a key element of the covariance matrix of the power spectrum. In this paper, we present explicit calibrations of the EFT counterterms for the one-loop trispectrum. Specifically, we find clear evidence for non-zero EFT corrections. We define two one-parameter ans\"{a}tze for the counterterm of the one-loop propagator and show that they provide a good correction to the residual at scales below k~0.07 h/Mpc. We then take the amplitudes of the linear and quadratic counterkernels calculated in our previous paper on the bispectrum and use them in the remaining counterterms, establishing consistency of the counterterms in the two, three and four point function. We also show that the commonly used EdS approximation for the growth of the density fields leads to errors that are of the same magnitude as loop corrections to the trispectrum on large scales.