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 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.
Highlights
The “2-Parameter Perturbation Theory” (2PPT) was recently introduced in order to provide a mathematical framework in which to understand and study this problem [6, 7]
We find that the time-dependence that the presence of a non-zero cosmological constant induces into the first-order gravitational potentials significantly complicates the application of the 2-parameter perturbation theory (2PPT) equations, and increases the disparity between this approach and the more traditional use of second-order cosmological perturbation theory
Absorbing the parts of θ(1) and δ(1) that behave like the first-approximations to the corresponding Newtonian quantities into θN(1) and δ(N1) gives us that only remaining non-Newtonian part of these quantities is given by δ(1) = −2φ. This process of re-defining Newtonian quantities to absorb the long-wavelength parts of the corresponding large-scale perturbations is described in more detail in Equations (5.12)-(5.16) of Ref. [9], and proceeds in exactly the same way here. These results show that the first approximation to the 2PPT equations gives identical results to standard first-order cosmological perturbation theory in a ΛCDM universe
Summary
Two-parameter perturbation theory is constructed by performing post-Newtonian and cosmological perturbation theory expansions around a single Friedmann background, which results in a line-element that can be written in longitudinal gauge as [7]. Ds2 = a(τ ) − (1 + 2U + 2φ)dτ 2 + (1 − 2U − 2ψ)δijdxidxj. We will briefly outline the equations that must be obeyed in the presence of a non-zero Λ by the Newtonian potential U , the scale factor a, and the large-scale cosmological perturbations φ and ψ. More thorough mathematical treatment, justification and introduction, the reader is referred to Ref. More thorough mathematical treatment, justification and introduction, the reader is referred to Ref. [7]
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