Loop Corrections in Nonlinear Cosmological Perturbation Theory. II. TwoPoint Statistics and SelfSimilarity
Abstract
We calculate the lowest order nonlinear contributions to the power spectrum, twopoint correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scalefree initial power spectra, P(k) ~k^n^. These results extend and, in some cases, correct previous work in the literature on cosmological perturbation theory. Comparing with the scaling behavior observed in Nbody simulations, we find that the validity of nonlinear perturbation theory depends strongly on the spectral index n. For n < 1, we find excellent agreement over scales where the variance σ^2^(R) <~ 10; however, for n >= 1, perturbation theory predicts deviations from selfsimilar scaling (which increase with n) not seen in numerical simulations. This anomalous scaling suggests that the principal assumption underlying cosmological perturbation theory, namely, that largescale fields can be described perturbatively even when fluctuations are highly nonlinear on small scales, breaks down beyond leading order for spectral indices n >= 1. For n <  1, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1996
 DOI:
 10.1086/178177
 arXiv:
 arXiv:astroph/9602070
 Bibcode:
 1996ApJ...473..620S
 Keywords:

 GALAXIES: CLUSTERS: GENERAL;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 METHODS: NUMERICAL;
 Astrophysics
 EPrint:
 48 pages, 19 figures, uses axodraw.sty