Open AccessEvolution of the cosmological density distribution function
Author(s) -
Taylor A. N.,
Watts P. I. R.
Publication year - 2000
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2000.03339.x
Subject(s) - physics , probability density function , statistical physics , skewness , cosmological perturbation theory , perturbation (astronomy) , distribution function , perturbation theory (quantum mechanics) , probability distribution , distribution (mathematics) , eulerian path , dark matter , classical mechanics , cosmology , mathematical physics , mathematical analysis , astrophysics , quantum mechanics , statistics , mathematics , lagrangian
We present a new calculation for the evolution of the one‐point probability distribution function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman–Kolmogorov equation and second‐order Eulerian perturbation theory we propagate the initial density distribution into the non‐linear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependence on the initial perturbation spectrum. We compare our results with other approximations to the one‐point PDF, and with N ‐body simulations. We find that our distribution accurately models the evolution of the one‐point PDF of dark matter.