The Intrinsic Matter Bispectrum in $\Lambda$CDM

TL;DR

This paper presents a comprehensive relativistic calculation of the matter bispectrum in the $\Lambda$CDM model, incorporating baryons and dark matter, with improved analytic approximations and analysis of baryon acoustic oscillation effects.

Contribution

It provides the first full numerical integration of the matter bispectrum for baryons and dark matter using the SONG code, along with an improved analytic kernel that accounts for various relativistic effects.

Findings

The improved kernel fits numerical results at percent level accuracy.

Baryon acoustic oscillations significantly influence the bispectrum, especially in squeezed configurations.

Relativistic effects and radiation impact the matter bispectrum at different epochs.

Abstract

We present a fully relativistic calculation of the matter bispectrum at second order in cosmological perturbation theory assuming a Gaussian primordial curvature perturbation. For the first time we perform a full numerical integration of the bispectrum for both baryons and cold dark matter using the second-order Einstein-Boltzmann code, SONG. We review previous analytical results and provide an improved analytic approximation for the second-order kernel in Poisson gauge which incorporates Newtonian nonlinear evolution, relativistic initial conditions, the effect of radiation at early times and the cosmological constant at late times. Our improved kernel provides a percent level fit to the full numerical result at late times for most configurations, including both equilateral shapes and the squeezed limit. We show that baryon acoustic oscillations leave an imprint in the matter bispectrum, making a significant impact on squeezed shapes.