X iv : g r - qc / 9 30 40 22 v 1 1 6 A pr 1 99 3 SCALING PROPERTIES OF GRAVITATIONAL CLUSTERING IN THE NON - LINEAR REGIME
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چکیده
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) ≡ −[v/(˙ ax)] depends on the expansion factor a and comoving coordinate x only through the density contrast σ(a, x). This leads to the result that the true, non-linear, density contrast < (δρ/ρ) 2 x > 1/2 = σ(a, x) is a universal function of the density contrast σ L (a, l), computed in the linear theory and evaluated at a scale l where l = x(1 + σ 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[σ 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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تاریخ انتشار 1993