The Bispectrum: From Theory to Observations

By R. Scoccimarro. 2000

170 citations recorded by the source corpus.

The bispectrum is the lowest order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the bispectrum is well understood theoretically from nonlinear perturbation theory and numerical simulations, applications to galaxy surveys require a number of issues to be addressed. In this paper we consider the effect on the bispectrum of stochastic nonlinear biasing, radial redshift distortions, non-Gaussian initial conditions, survey geometry, and sampling. We find that: (1) Bias stochasticity does not affect the use of the bispectrum to recover the mean biasing relation between galaxies and mass, at least for models in which the scatter is uncorrelated at large scales. (2) Radial redshift distortions do not significantly change the monopole power spectrum and bispectrum compared to their plane-parallel values. (3) Survey geometry leads to finite-volume effects, which must be taken into account in current surveys before comparison with theoretical predictions can be made. (4) Sparse sampling and survey geometry correlate different triangles, leading to a breakdown of the Gaussian likelihood approximation. We develop a likelihood analysis using bispectrum eigenmodes, calculated by Monte Carlo realizations of mock surveys generated with second-order Lagrangian perturbation theory and checked against N-body simulations. In a companion paper, we apply these results to the analysis of the bispectrum of IRAS galaxies.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bd0d04d4439fed89a033a36049a5c5c5b498b8cd

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Citations in the corpus

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies (2016, background): “It was not until the late 1990s when perturbative models were developed (Matarrese et al. 1997; Scoccimarro et al. 1998; Heavens et al. 1998; Verde et al. 1998; Scoccimarro et al. 1999; Scoccimarro 2000) that enabled the galaxy bispectrum to be used for accurate cosmological predictions.”
PTHALOS: a fast method for generating mock galaxy distributions (2001, methodology): “This reproduces the correct two and three-point statistics at large scales, and approximates the four-point and higher-order statistics very well (Moutarde et al. 1991; Buchert et al. 1994; Bouchet et al. 1995; Scoccimarro 2000).”
Analysis of Systematic Effects and Statistical Uncertainties in Angular Clustering of Galaxies from Early Sloan Digital Sky Survey Data (2001, methodology): “…distribution using second-order Lagrangian perturbation theory (2LPT), which reproduces the correct twoand three-point statistics at large scales and approximates four-point statistics and higher (Moutarde et al. 1991; Buchert, Melott, & Weiss 1994; Bouchet et al. 1995; Scoccimarro 2000) very well.”
Accurate estimators of correlation functions in Fourier space (2015, methodology): “Along the lines of the tests presented in Colombi et al. (2009), in this section we consider two different particle distributions both relevant for Large-Scale Structure studies: a N-body simulation evolved to redshift zero on a relatively small box (therefore characterized by significant non-linear”
Transients from initial conditions in cosmological simulations (2006, methodology): “(3) is given by (see Scoccimarro (2000) for a detailed derivation) Ψa(k, η) = gab(η) φb(k) + ∫ η 0 dη′ gab(η − η′) ×γ(s)bcd(k,k1,k2)Ψc(k1, η ′)Ψd(k2, η ′), (7) where φa(k) ≡ Ψa(k, η = 0) denotes the initial conditions, set when the linear growth factor a(τ ) = 1 and η = 0.”
The power spectrum and bispectrum of SDSS DR11 BOSS galaxies – I. Bias and gravity (2014, background): “…probe galaxy bias from galaxy redshift surveys, a full treatment of the redshift-space bispectrum for galaxies had to be developed (Matarrese, Verde & Heavens 1997; Heavens, Matarrese & Verde 1998; Scoccimarro et al. 1998; Verde et al. 1998; Scoccimarro, Couchman & Frieman 1999; Scoccimarro 2000).”
The 2dF Galaxy Redshift Survey: The bias of galaxies and the density of the Universe (2001, methodology): “The galaxies are weighted with the optimum weight for measuring the power spectrum (Feldman, Kaiser & Peacock 1994), which also minimises the variance of higher-order correlation functions (Scoccimarro 2000).”
DENSITY STUDIES OF MHD INTERSTELLAR TURBULENCE: STATISTICAL MOMENTS, CORRELATIONS AND BISPECTRUM (2008, methodology): “The bispectrum has been widely used in cosmology and gravitational wave studies (Fry 1998; Scoccimarro 2000; Liguori et al. 2006) and for the characterization of wave-wave interactions in laboratory plasmas (Intrator et al. 1989; Tynan et al. 2001), 5 The first mentioning of the effect can be…”
Effects of scale-dependent non-Gaussianity on cosmological structures (2007, unknown): “Contents”
The bispectrum in the Effective Field Theory of Large Scale Structure (2014, methodology): “of shells. A naive implementation of the above estimator is very slow, since one would have to check N2 c cells for the triangle condition. Rewriting the Dirac delta as an integral we have (see Refs. [35,36]) B^(k i;kj;kl) = V f Vijl Z x Y =i;j;l Z [q] exp[iqx](q) (5.3) Thus, we are selecting Fourie”
Bayesian physical reconstruction of initial conditions from large-scale structure surveys (2012, methodology): “…the exact one- and three-point statistics of fully non-linear density fields at large scales, and also approximates higher order statistics very well (see e.g. Moutarde et al. 1991; Buchert et al. 1994; Bouchet et al. 1995; Scoccimarro 2000; Bernardeau et al. 2002; Scoccimarro & Sheth 2002).”
Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure (2010, methodology): “As already mentioned, measurements of triangular configurations different in shape and size allow to disentangle the different sources of non-Gaussianity and determine independently b1 and b2, provided that accurate predictions for the matter bispectrum, from PT or N-body simulations, are available ”