The three‐point correlation function in cosmology

By M. Takada, B. Jain. 2002

169 citations recorded by the source corpus.

With the advent of high-quality surveys in cosmology, the full three-point correlation function (3PCF) will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo properties that cannot be extracted from the two-point correlation function. We use the halo clustering model to calculate the three-point correlation function analytically for general cosmological fields. We present detailed results for the configuration dependence of the three-dimensional mass and galaxy distributions and the two-dimensional cosmic shear field. We work in real space, where higher order correlation functions on small scales are easier to measure and interpret, but halo model calculations become rapidly intractable. Hence we develop techniques that allow for the accurate evaluation of all the contributing terms to real-space correlations. We apply them to the 3PCF to show how its configuration and scale dependence change as one transits from the non-linear to the quasilinear regime, and how this depends on the relative contributions from the one-, two- and three-halo terms. The 3PCF violates the hierarchical Ansatz in both its scale and configuration dependence. We study the behaviour of the coefficient Q in the expansion: ζ(r 1 2 , r 2 3 , r 3 1 ) = Q[ξ(r 1 2 ) ξ(r 2 3 ) + ξ(r 1 2 )ξ(r 3 1 ) + ξ(r 2 3 )ξ(r 3 1 )] from large, quasilinear scales down to approximately 20 kpc. We find that the non-linear 3PCF is sensitive to the halo profile of massive haloes, especially its inner slope. We model the distribution of galaxies in haloes and show that the 3PCF of red galaxies has a weaker configuration and scale dependence than the mass, while for blue galaxies it is very sensitive to the parameters of the galaxy formation model. The 3PCF from weak lensing on the other hand shows different scalings arising from projection effects and a sensitivity to cosmological parameters. We discuss how our results can be applied to various analytical calculations: covariances of the two-point correlation function, the pairwise peculiar velocity dispersion, higher order shear correlations, and to extend the halo model by including the effects of halo triaxiality and substructure on statistical measures.

Subfields: Astronomy and Astrophysics, Ecology, Plant Science

View Paper: https://www.semanticscholar.org/paper/0c92b16a46657c30b1dec0eba772260ce2fdcaa2

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Citations in the corpus

Cosmology with the shear-peak statistics (2009, methodology): “Cosmic shear can access information about the non-Gaussianity of the matter distribution only through higher order correlation functions (see e.g. Takada & Jain 2003 for constraints using the three-point correlation function).”
Cosmological parameters from lensing power spectrum and bispectrum tomography (2003, background): “The bispectrum is the lowest-order quantity to extract non-Gaussianity in the weak l nsing field, and thus provides additional information on structure formation models relative to the power spectrum (e.g., Takada & Jain 2002, 2003a,b,c, hereafter TJ02 and TJ03a,b,c).”
Towards a concordant model of halo occupation statistics (2006, background): “Additional constraints on the higher moments of P(N | M) can be obtained from the n-point correlation functions with n 3 (Takada & Jain 2003; Zheng 2004b).”
Combining Lens Distortion and Depletion to Map the Mass Distribution of A1689 (2007, methodology): “Alternatively, a truncated NFW profile can be used to model the convergence profile (Takada & Jain 2003).”
Detailed cluster lensing profiles at large radii and the impact on cluster weak lensing studies (2011, background): “The lensing properties of this profile can also be computed analytically (see Takada & Jain 2003a,b).”
On Departures from a Power Law in the Galaxy Correlation Function (2003, methodology): “Second, we approximately incorporate the effects of halo exclusion by including in the two-halo term at separation r only those halos whose virial radii are Rvir r=2 (similar to Takada & Jain 2003).”
The impact of non‐Gaussian errors on weak lensing surveys (2008, methodology): “(2) For the different halo terms (2-halo term etc.), there are uncertainties in the model, such as the halo exclusion effect (Takada & Jain 2003a; Fosalba et al. 2005).”
The Luminosity and Color Dependence of the Galaxy Correlation Function (2004, background): “Three-point correlations probe the high-mass regime of P(N |M ) (Ma & Fry 2000; Scoccimarro et al. 2001; LUMINOSITY AND COLOR DEPENDENCE 25No. 1, 2005 Takada & Jain 2003), and they provide a diagnostic for the amplitude of dark matter fluctuations (Fry 1994; Feldman et al. 2001; Verde et al. 2002).”
LoCuSS: Subaru Weak Lensing Study of 30 Galaxy Clusters (2009, methodology): “I MΔ; cΔ/, given the NFW profile (Bartelmann 1996; Wright & Brainerd 2000; Takada & Jain 2003).”
Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, methodology): “…methods that have been advocated and which typically involve adopting an upper limit for the mass interval used in the integral for the 2-halo term of the power spectrum (e.g., Takada & Jain 2003; Zheng 2004; Abazajian et al. 2005; Tinker et al. 2005, 2012; Yoo et al. 2006; Leauthaud et al. 2011).”
SIMULATIONS OF WIDE-FIELD WEAK LENSING SURVEYS. I. BASIC STATISTICS AND NON-GAUSSIAN EFFECTS (2009, methodology): “The details of our halo model implementation can be found in Takada & Jain (2003a) (also see Takada & Jain 2003b).”
Cosmology from the Chinese Space Station Optical Survey (CSS-OS) (2019, methodology): “…spectrum, the CSS-OS three-dimensional (3-d) galaxy clustering data also can be analyzed using other methods, such as topology (Park & Kim 2010), tomographic Alcock-Paczynski (Li et al. 2016) and 3-point correlation function (Takada & Jain 2003), that can extract more cosmological information.”
The Intrinsic Alignment of Galaxies and its Impact on Weak Gravitational Lensing in an Era of Precision Cosmology (2014, background): “…of large-scale structure (Bernardeau et al., 1997; van Waerbeke et al., 1999; Matarrese et al., 2000; Van Waerbeke et al., 2001; Verde et al., 2001; Takada and Jain, 2003, 2004; Munshi et al., 2008; Jeong and Komatsu, 2009; Vafaei et al., 2010; Huterer et al., 2011; Semboloni et al., 2011; Heymans…”