Clarksona, ChrisGallagher, Christopher S.Clifton, Timothy2021-02-182021-02-182020Clarksona, C. et al. (2020). Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era. Journal of Cosmology and Astroparticle Physics ,2020(03)http://doi.org/10.1088/1475-7516/2020/03/011http://hdl.handle.net/10566/5958Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales (< 100 Mpc), 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.enCosmological perturbation theoryGravityNon-gaussianityPower spectrumNonlinear densityArticle