The Angular Three‐Point Correlation Function in the Quasi‐linear Regime

Buchalter, Ari; Kamionkowski, Marc; Jaffe, A. H.

doi:10.1086/308339

Cited by 29 publications

(33 citation statements)

References 86 publications

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“…As a consequence the skewness of κ is expected to display a strong Ω m dependence. This property has indeed been found in [53] where it has been shown using PT that for sources at redshift unity 101 . This result has been subsequently extended to the nonlinear regime [339,326,467,469,666,158], higher-order moments, the bispectrum [158], and to more complex quantities such as the shape of the one-point PDF of the convergence field [658,659,468].…”

Section: Statistical Propertiessupporting

confidence: 75%

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Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

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Section: Statistical Propertiessupporting

confidence: 75%

“…As expected, similar results hold for the hierarchy of correlation functions in the weakly non-linear regime. The results for the angular three-point function and bispectrum have been studied with most detail [242,225,101,671]. From Eqs.…”

Section: The Correlation Hierarchy For the Projected Densitymentioning

confidence: 99%

Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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“…Gaztañaga and Scoccimarro 2005). The projected three-point correlation can also be studied separated by in redshift bins (Frieman and Gaztañaga 1999;Buchalter et al 2000;Zheng 2004). Both ways will result in larger errors, but we do not expect this to be a limitation because our error budget is totally dominated by the uncertainty in the bias.…”

Section: Summary and Discussionmentioning

confidence: 99%

Measuring the growth of matter fluctuations with third-order galaxy correlations

Hoffmann

Bel

Gaztañaga

et al. 2014

Monthly Notices of the Royal Astronomical Society

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Measurements of the linear growth factor D at different redshifts z are key to distinguish among cosmological models. One can estimate the derivative dD(z)/d ln(1 + z) from redshift space measurements of the 3D anisotropic galaxy two-point correlation ξ(z), but the degeneracy of its transverse (or projected) component with galaxy bias, introduces large errors in the growth measurement.Here we present a comparison between two methods which break this degeneracy by combining second-and third-order statistics. One uses the shape of the reduced three-point correlation and the other a combination of third-order one-and two-point cumulants. These methods use the fact that, for Gaussian initial conditions and scales larger than 20 h −1 Mpc, the reduced third-order matter correlations are independent of redshift (and therefore of the growth factor) while the third-order galaxy correlations depend on b. We use matter and halo catalogs from the MICE-GC simulation to test how well we can recover b(z) and therefore D(z) with these methods in 3D real space. We also present a new approach, which enables us to measure D directly from the redshift evolution of second-and third-order galaxy correlations without the need of modelling matter correlations.For haloes with masses lower than 10 14 h −1 M ⊙ , we find 10% deviations between the different estimates of D, which are comparable to current observational errors. At higher masses we find larger differences that can probably be attributed to the breakdown of the bias model and non-Poissonian shot noise.

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“…(e.g., Refs. [43,[46][47][48][49][50][51][52][53][54][55][56][57][58]). This formalism can be extended to include stochasticity by formulating the biasing in terms of the conditional probability distribution Pð g;h j m Þ of g;h at a given m (e.g., Ref.…”

Section: Introductionmentioning

confidence: 99%

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

2010

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Models of galaxy and halo clustering commonly assume that the tracers can be treated as a continuous field locally biased with respect to the underlying mass distribution. In the peak model pioneered by Bardeen et al. (1986), one considers instead density maxima of the initial, Gaussian mass density field as an approximation to the formation site of virialized objects. In this paper, the peak model is extended in two ways to improve its predictive accuracy. Firstly, we derive the two-point correlation function of initial density peaks up to second order and demonstrate that a peak-background split approach can be applied to obtain the k-independent and k-dependent peak bias factors at all orders. Secondly, we explore the gravitational evolution of the peak correlation function within the Zel'dovich approximation. We show that the local (Lagrangian) bias approach emerges as a special case of the peak model, in which all bias parameters are scale-independent and there is no statistical velocity bias. We apply our formulae to study how the Lagrangian peak biasing, the diffusion due to large scale flows and the mode-coupling due to nonlocal interactions affect the scale dependence of bias from small separations up to the baryon acoustic oscillation (BAO) scale. For 2σ density peaks collapsing at z = 0.3, our model predicts a ∼5% residual scale-dependent bias around the acoustic scale that arises mostly from first-order Lagrangian peak biasing (as opposed to second-order gravity mode-coupling). We also search for a scale dependence of bias in the large scale auto-correlation of massive halos extracted from a very large N-body simulation provided by the MICE collaboration. For halos with mass M 10 14 M⊙/h, our measurements demonstrate a scale-dependent bias across the BAO feature which is very well reproduced by a prediction based on the peak model.

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The Angular Three‐Point Correlation Function in the Quasi‐linear Regime

Cited by 29 publications

References 86 publications

Large-scale structure of the Universe and cosmological perturbation theory

Large-scale structure of the Universe and cosmological perturbation theory

Measuring the growth of matter fluctuations with third-order galaxy correlations

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

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