Analysis of two-point statistics of cosmic shear - I. Estimators and covariances

By P. Schneider, L. Waerbeke, M. Kilbinger, Yannick Mellier Iaef, Bonn, Mpa, Garching, Aip, París, Cita and 2 more. 2002

158 citations recorded by the source corpus.

Recently, cosmic shear, the weak lensing effect by the inhomogeneous matter distribution in the Universe, has not only been detected by several groups, but the observational results have been used to derive constraints on cosmological parameters. For this purpose, several cosmic shear statistics have been employed. As shown recently, all second-order statistical measures can be expressed in terms of the two-point correlation functions of the shear, which thus represents the basic quantity; also, from a practical point-of-view, the two-point correlation functions are easiest to obtain from observational data which typically have complicated geometry. We derive in this paper expressions for the covariance matrix of the cosmic shear two- point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry which allows us to obtain approximations for the covariance matrix in terms of integrals which are readily evaluated numerically. These results are then used to study the covariance of the aperture mass dispersion which has been employed earlier in quantitative cosmic shear analyses. We show that the aperture mass dispersion, measured at two different angular scales, quickly decorrelates with the ratio of the scales. Inverting the relation between the shear two-point correlation functions and the power spectrum of the underlying projected matter distribution, we construct estimators for the power spectrum and for the band powers, and show that they yields accurate approximations; in particular, the correlation between band powers at different wave numbers is quite weak. The covariance matrix of the shear correlation function is then used to investigate the expected accuracy of cosmological parameter estimates from cosmic shear surveys. Depending on the use of prior information, e.g. from CMB measurements, cosmic shear can yield very accurate determinations of several cosmological parameters, in particular the normalization σ8 of the power spectrum of the matter distribution, the matter density parameter Ωm, and the shape parameter Γ.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/622846062c0fb612a813ec47905de076b713e5dd

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Citations in the corpus

Gravitational lensing analysis of the Kilo-Degree Survey (2015, background): “…extract cosmological parameter constraints and information about systematics from the data, a wide range of different two-point statistics have been proposed (see Schneider et al. 2002b; Schneider, Eifler & Krause 2010, for a comprehensive discussion of the relationship between these statistics).”
KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters (2017, methodology): “Alternative pseudo-C( ) methods are based on correlationfunction measurements as input (e.g. Schneider et al. 2002; Becker et al. 2016).”
CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments (2013, methodology): “(3) There are a range of different two-point statistics that have been proposed to extract weak lensing information from the data (see Schneider et al. 2002, 2010, for a comprehensive discussion of the relationship between these statistics).”
Cosmological constraints from cosmic shear two-point correlation functions with HSC survey first-year data (2019, methodology): “For the measurement of the TPCFs themselves, we used the public software Athena2 (Schneider et al. 2002).”
KiDS+GAMA : cosmology constraints from a joint analysis of cosmic shear, galaxy-galaxy lensing, and angular clustering (2017, methodology): “1 http://euclid-ec.org 2 https://www.lsst.org/ 3 https://wfirst.gsfc.nasa.gov/ In this work, we adopt a formalism from Schneider et al. (2002) to estimate power spectra by performing simple integrals over the real-space correlation functions using appropriate weight functions.”
Why your model parameter confidences might be too optimistic - unbiased estimation of the inverse covariance matrix (2006, methodology): “An example from the field of weak gravitational lensing is Semboloni et al. (2006), who use th Gaussian approximation to the covariance matrix of the shear correlation functions given by Schneider et al. (2002).”
Intrinsic alignments of SDSS-III BOSS LOWZ sample galaxies (2014, background): “In the shape noise-dominated limit, in the case that the shape and density sample are the same, the standard deviations of wg+ and w++ are proportional to σγ and σ 2 γ (see, e.g., Schneider et al. 2002), respectively, where σγ is the shape noise per component for our sample.”
Cosmological constraints from the 100-deg2 weak-lensing survey (2007, methodology): “For the first time we account for the effects of non-Gaussian contributions to the analytic estimate of the sample variance – sometimes referred to as cosmic variance – covariance matrix (Schneider et al. 2002), as described in Semboloni et al. (2007).”
First Cosmic Shear Results from the Canada-France-Hawaii Telescope Wide Synoptic Legacy Survey (2005, methodology): “Expressions for T (x) can be found in Crittenden et al. (2002) and Schneider et al. (2002b).”
KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing (2016, background): “Schneider et al. (2002b) and Schneider, Eifler & Krause (2010) discuss the relationship between a number of different real-space two-point statistics.”
CFHTLenS: the Canada–France–Hawaii Telescope Lensing Survey – imaging data and catalogue products (2012, methodology): “One drawback however is that to avoid bias in the E/B measurement from data, the most typically used E/B mode decomposition method from Schneider et al. (2002) formally requires an input cosmology which we generally wish to avoid using in our blind systematics tests (see for example Kilbinger et…”
Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime (2007, methodology): “The covariance matrices for the shear two-point correlation functions are calculated using the expressions of Schneider et al. (2002a), valid for a Gaussian shear field.”
CFHTLenS: combined probe cosmological model comparison using 2D weak gravitational lensing (2012, background): “The filter functions for the aperture-mass dispersion, defined in Schneider et al. (2002a), are for x < 2 T+(x) = 6(2 − 15x 2) 5 [ 1 − 2 π arcsin(x/2) ] + x √ 4 − x2 100π × (120 + 2320x2 − 754x4 + 132x6 − 9x8) ; T−(x) = 192 35π x3 ( 1 − x 2 4 )7/2 .”
Weak-Lensing Results from the 75 Square Degree Cerro Tololo Inter-American Observatory Survey (2003, methodology): “Another advantage to using the Map statistic is that Map(h1) is very weakly correlated with Map(h2) when h1 differs from h2 by a factor of 2 (Schneider et al. 2002a).”
Galaxy Alignments: Observations and Impact on Cosmology (2015, background): “…j|), where δi j is the Kronecker delta, σ denotes the total intrinsic ellipticity dispersion, and the angle brackets indicate an ensemble average over the intrinsic ellipticity distribution and over the cosmic shear field, assuming randomly-oriented intrinsic ellipticities (Schneider et al. 2002a).”
Weak Gravitational Lensing by Large-Scale Structure (2003, methodology): “These techniques have also been used to compute the full probability distribution function of the convergence field (Bernardeau & Valageas 2000, Munshi & Jain 2000, Valageas 2000) and the errors in two-point statistics (Cooray & Hu 2001b; Munshi & Coles 2002; Schneider et al. 2002).”