Open AccessPower transfer in non‐linear gravitational clustering and asymptotic universality
Author(s) -
Padmanabhan T.,
Ray Suryadeep
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society: letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.067
H-Index - 122
eISSN - 1745-3933
pISSN - 1745-3925
DOI - 10.1111/j.1745-3933.2006.00225.x
Subject(s) - physics , gravitation , spectral density , universality (dynamical systems) , fourier transform , mathematical physics , differential equation , mathematical analysis , statistical physics , classical mechanics , quantum mechanics , mathematics , statistics
We study the non‐linear gravitational clustering of collisionless particles in an expanding background using an integro‐differential equation for the gravitational potential. In particular, we address the question of how the non‐linear mode–mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self‐similar evolution for the gravitational potential φ k ( t ) in Fourier space of the form φ k ( t ) = F ( t ) D ( k ) where the function F ( t ) satisfies a second‐order non‐linear differential equation. We analyse the relevant solutions of this equation, thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis suggests that both F ( t ) and D ( k ) have well‐defined asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations, showing good agreement over the range at which we could test them.