Multi-scale perturbation theory II: Solutions and leading-order bispectrum in the ΛcDM universe
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 ΛCDM 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 secondorder 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