NDLI: Analysis of two-point statistics of cosmic shear

Content Provider	EDP Sciences
Author	P. Schneider L. van Waerbeke M. Kilbinger Y. Mellier
Abstract	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 of the power spectrum of the matter distribution, the matter density parameter , and the shape parameter Γ.
Ending Page	19
Starting Page	1
Page Count	19
File Format	HTM / HTML PDF
ISSN	00046361
Alternate Webpage(s)	https://www.aanda.org/articles/aa/abs/2002/46/aah3767/aah3767.html
e-ISSN	14320746
Issue Number	1
Journal	Astronomy & Astrophysics
Volume Number	396
DOI	10.1051/0004-6361:20021341
Language	English
Publisher	EDP Sciences
Publisher Date	2002-12-01
Access Restriction	Open
Rights Holder	© ESO, 2002
Subject Keyword	dark matter gravitational lensing large-scale structure of the Universe dark matter / gravitational lensing / large-scale structure of the Universe
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics Space and Planetary Science

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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