paper

Multi-Scale Perturbation Theory I: Methodology and Leading-Order Bispectrum Corrections in the Matter-Dominated Era

arXiv:1910.04894 · doi:10.1088/1475-7516/2020/03/011

Abstract

Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales (), whilst retaining a traditional approach to cosmological perturbations in the long-wavelength universe. In this paper we study the solutions that arise from this theory in a spatially-flat dust-filled cosmology, and what these imply for the bispectrum of matter. This is achieved by using Newtonian perturbation theory to model the gravitational fields of nonlinear structures in the quasi-linear regime, and then using the resulting solutions as source terms for the cosmological equations. We find that our approach results in the leading-order part of the cosmological gravitational potentials being identical to those that result from standard cosmological perturbation theory at second-order, while the dark matter bispectrum itself yields some differences on Hubble scales. This demonstrates that our approach is sufficient to capture most leading-order relativistic effects, but within a framework that is far easier to generalize. We expect this latter property to be particularly useful for calculating leading-order relativistic corrections to the matter power spectrum, as well as for deriving predictions for relativistic effects in alternative theories of gravity.

arXiv comment51 pages, 14 figures

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