Cosmological perturbations: Entering the nonlinear regime

被引:69
作者
Scoccimarro, R
机构
[1] UNIV CHICAGO, DEPT PHYS, CHICAGO, IL 60637 USA
[2] UNIV CHICAGO, ENRICO FERMI INST, CHICAGO, IL 60637 USA
[3] FERMILAB NATL ACCELERATOR LAB, NASA, FERMILAB ASTROPHYS CTR, BATAVIA, IL 60510 USA
关键词
cosmology; theory; large-scale structure of the universe; methods; numerical;
D O I
10.1086/304578
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We consider next-to-leading-order (one-loop) nonlinear corrections to the bispectrum and skewness of cosmological density fluctuations induced by gravitation evolution, focusing on the case of Gaussian initial conditions and scale-free initial power spectra, P(k) proportional to k ''. As has been established by comparison with numerical simulations, leading order (tree-level) perturbation theory describes these quantities at the largest scales. The one-loop perturbation theory provides a tool to probe the transition to the nonlinear regime on smaller scales. In this work, we find that, as a function of spectral index n, the one-loop bispectrum follows a pattern analogous to that of the one-loop power spectrum, which shows a change in behavior at a ''critical index'' n(c) approximate to -1.4, where nonlinear corrections vanish. The tree-level perturbation theory predicts a characteristic dependence of the bispectrum on the shape of the triangle defined by its arguments. For n less than or similar to n(c), one-loop corrections increase this configuration dependence of the leading order contribution; for n greater than or similar to n(c), one-loop corrections tend to cancel the configuration dependence of the tree-level bispectrum, in agreement with known results from n = -1 numerical simulations. A similar situation is shown to hold for the Zeldovich approximation, where n(c) approximate to -1.75. We obtain explicit analytic expressions for the one-loop bispectrum for n = -2 initial power spectra, for both the exact dynamics of gravitational instability and the Zeldovich approximation. We also compute the skewness factor, including local averaging of the density field, for n = -2: S-3(R) = 4.02 + 3.83 sigma(G)(2)(R) for Gaussian smoothing and S-3(R) = 3.86 + 3.18 sigma(TH)(2)(R) for top-hat smoothing, where sigma(2)(R) is the variance of the density field fluctuations smoothed over a window of radius R. A comparison with fully nonlinear numerical simulations implies that, for n < -1, the one-loop perturbation theory can extend our understanding of nonlinear clustering down to scales where the transition to the stable clustering regime begins.
引用
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页码:1 / 17
页数:17
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