Scaling properties of the gravitational clustering in the nonlinear regime

Details Scaling properties of the gravitational clustering in the nonlinear regime Scaling properties of the gravitational clustering in the nonlinear regime

1993-04-16

arxiv.org/abs/gr-qc/9304022v1

Mon.Not.Roy.Astron.Soc. 271 (1994) 976

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages 2 figures available on request, TeX, IUCAA-12/93

Scientific paper

The growth of density perturbations in an expanding universe in the non-linear regime is investigated. The underlying equations of motion are cast in a suggestive form, and motivate a conjecture that the scaled pair velocity, $h(a,x)\equiv -[v/(\dot{a}x)]$ depends on the expansion factor $a$ and comoving coordinate $x$ only through the density contrast $\sigma(a,x)$. This leads to the result that the true, non-linear, density contrast $<(\delta\rho/\rho)^{2}_{x}>^{1/2}=\sigma(a,x)$ is a universal function of the density contrast $\sigma_L(a,l)$, computed in the linear theory and evaluated at a scale $l$ where $l=x(1+\sigma^2)^{1/3}$. This universality is supported by existing numerical simulations with scale-invariant initial conditions having different power laws. We discuss a physically motivated ansatz $h(a,x)=h[\sigma^2(a,x)]$ and use it to compute the non-linear density contrast at any given scale analytically. This provides a promising method for analysing the non-linear evolution of density perturbations in the universe and for interpreting numerical simulations.

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