Multi-Scale Perturbation Theory II: Solutions and Leading-Order Bispectrum in the $\Lambda$CDM Universe

TL;DR

This paper applies a two-parameter perturbation theory framework to compute the matter bispectrum in a $\\Lambda$CDM universe, bridging small-scale nonlinear effects with large-scale cosmological perturbations.

Contribution

It introduces a novel application of 2PPT to calculate the matter bispectrum, combining Newtonian and relativistic effects in a unified formalism.

Findings

Reproduces some relativistic effects from second-order perturbation theory

Demonstrates the feasibility of modeling both linear and nonlinear structures simultaneously

Provides a foundation for more comprehensive relativistic cosmological analyses

Abstract

Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to calculate and study the bispectrum of matter in a spatially-flat $\Lambda$CDM cosmology. This is achieved by deploying Newtonian perturbation theory to model the gravitational fields of quasi-nonlinear structures, and then subsequently using them as source terms for the large-scale cosmological perturbations. We find that our approach reproduces some of the expected relativistic effects from second-order cosmological perturbation theory, but not all. This work therefore provides a first step in deploying a formalism that can simultaneously model the weak gravitational fields of both linear and nonlinear structures in a realistic model of the Universe.