An application of the wiener hermite expansion to the nonlinear evolution of dark matter

N. S. Sugiyama, T. Futamase

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10 Citations (Scopus)


We apply the Wiener Hermite (WH) expansion to the nonlinear evolution of the large-scale structure and obtain an approximate expression for the matter power spectrum in the full order of the expansion. This method allows us to expand any random function in terms of an orthonormal basis in the space of random functions in such a way that the first order of the expansion expresses the Gaussian distribution, and others are the deviations from Gaussianity. It is proved that the WH expansion is mathematically equivalent to the Γ-expansion approach in the renormalized perturbation theory (RPT). While exponential behavior in the high-k limit has been proved for the mass density and velocity fluctuations of dark matter in the RPT, we prove the behavior again in the context of the WH expansion using the result of the standard perturbation theory (SPT). We propose a new approximate expression for the matter power spectrum which interpolates the low-k expression corresponding to the 1-loop level in SPT and the high-k expression obtained by taking a high-k limit of the WH expansion. The validity of our prescription is specifically verified by comparing with the 2-loop solutions of the SPT. The proposed power spectrum agrees with the result of the N-body simulation with accuracy better than 1% or 2% in a range of baryon acoustic oscillation scales, where the wave number is about k = 0.2-0.4 h Mpc-1 at z = 0.5-3.0. This accuracy is comparable to or slightly less than the ones in the closure theory, the fractional difference of which from the N-body result is within 1%. One merit of our method is that the computational time is very short because only single and double integrals are involved in our solution.

Original languageEnglish
Article number114
JournalAstrophysical Journal
Issue number2
Publication statusPublished - 2012 Dec 1


  • dark matter
  • large-scale structure of universe

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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