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Evolution of Cosmological Density Distribution Function from the Local Collapse Model (2003)
BibTeX
@MISC{Ohta03evolutionof,
author = {Yasuhiro Ohta and Issha Kayo and Atsushi Taruya},
title = {Evolution of Cosmological Density Distribution Function from the Local Collapse Model},
year = {2003}
}
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Abstract
We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density δ and velocity-divergence fields θ. In particular, we derive an evolution equation for the one-point PDFs and consider the stochastic nature associated with these quantities. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the Lagrangian local dynamics with finite degrees of freedom, evolution equation for PDFs becomes a closed form and consistent formal solutions are constructed. Adopting this local approximation, we explicitly evaluate the onepoint PDFs P(δ) and P(θ) from the spherical and the ellipsoidal collapse models as the representative Lagrangian local dynamics. In a Gaussian initial condition, while the local density PDF from the ellipsoidal model almost coincides with the that of the spherical model, differences between spherical and ellipsoidal collapse model are found in the velocity-divergence PDF. These behaviors have also been confirmed from the perturbative analysis of higher order moments. Importantly,
Keyphrases
local collapse model cosmological density distribution function local approximation ellipsoidal collapse model evolution equation finite degree closed form onepoint pdfs perturbative analysis general framework consistent formal solution one-point probability distribution function ellipsoidal model one-point pdfs order moment cosmic fluid field local density pdf gaussian initial condition representative lagrangian local dynamic cosmic density velocity-divergence field lagrangian local dynamic spherical model stochastic nature velocity-divergence pdf
