Efficient Numerical Evaluation of a Two-Loop Contribution to the Dark-Matter Trispectrum

TL;DR

This paper presents a numerical method for efficiently evaluating a two-loop contribution to the dark-matter trispectrum by expanding around a reference cosmology, significantly reducing computational complexity.

Contribution

It introduces a perturbative expansion technique around a fixed reference cosmology to simplify and accelerate the calculation of the dark-matter trispectrum at two-loop order.

Findings

Third-order truncation achieves sub-percent accuracy

Expansion reduces the number of necessary computations

Method enables faster evaluations of higher-order correlators

Abstract

We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum of the target cosmology is written as a rescaled reference spectrum plus a small difference, and the trispectrum is expanded perturbatively in this difference. For the external momentum configuration considered here, truncating the expansion at third order reproduces the full numerical result with sub-percent accuracy over the range of scales studied, while higher-order terms are strongly suppressed. This reorganization reduces the number of cosmology-independent building blocks that must be computed compared with direct basis decompositions of the linear power spectrum. This provides a practical route to faster evaluations of higher-loop and higher-multiplicity correlators in the Effective Field Theory of Large-Scale Structure.