Weakly Nonlinear Clustering for Arbitrary Expansion Histories

We review the formalism and applications of the halo-based description of nonlinear gravitational clustering. In this approach, all mass is associated with virialized dark matter halos; models of the number and spatial distribution of the halos, and the distribution of dark matter within each halo, are used to provide estimates of how the statistical properties of large scale density and velocity fields evolve as a result of nonlinear gravitational clustering. We first describe the model, and demonstrate its accuracy by comparing its predictions with exact results from numerical simulations of nonlinear gravitational clustering. We then present several astrophysical applications of the halo model: these include models of the spatial distribution of galaxies, the nonlinear velocity, momentum and pressure fields, descriptions of weak gravitational lensing, and estimates of secondary contributions to temperature fluctuations in the cosmic microwave background.

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“…The bispectrum depends only weakly on Ω m , the only dependence coming from the fact that µ ≈ (3/7)Ω −2/63 m for 0.05 < Ω m < 3 [153].…”

Section: Results From Perturbation Theorymentioning

confidence: 98%

Halo models of large scale structure

2002

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“…Here the 2 permutations are k 3 ↔ k 1 , k 2 . Second order perturbation theory tells us that [38,39] …”

Section: F Pressure Bispectrummentioning

confidence: 99%

Large scale pressure fluctuations and the Sunyaev-Zel’dovich effect

Cooray

2000

Phys. Rev. D

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The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of the large scale structure gas distribution will be probed with current and upcoming wide-field small angular scale cosmic microwave background experiments. We study the generation of pressure fluctuations by baryons which are present in virialized dark matter halos, with overdensities > ∼ 200 and by baryons present in overdensities < ∼ 10. For collapsed halos, assuming the gas distribution is in hydrostatic equilibrium with matter density distribution, we predict the pressure power spectrum and bispectrum associated with the large scale structure gas distribution by extending the dark matter halo approach which describes the density field in terms of correlations between and within halos. The projected pressure power spectrum allows a determination of the resulting SZ power spectrum due to virialized structures. The unshocked photoionized baryons present in smaller overdensities trace the Jeans-scale smoothed dark matter distribution. They provide a lower limit to the SZ effect due to large scale structure in the absence of massive collapsed halos. We extend our calculations to discuss higher order statistics, such as bispectrum and skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a probe of correlations between dark matter and baryon density fields, while the probability distribution functions of peak statistics of SZ halos in wide field CMB data can be used as a probe of cosmology and non-Gaussian evolution of large scale pressure fluctuations.

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“…These kernels are correct for Q 0 ¼ 1, but are only weakly dependent on Q 0 (e.g. Bouchet et al 1992;Catelan et al 1995; see also Bernardeau 1994b, Eisenstein 1997and Kamionkowski & Buchalter 1998. After some manipulations, the transform of the third-order, biased, redshiftspace density field is…”

Section: Bias and Evolutionmentioning

confidence: 99%