Likelihood analysis of cosmic shear on simulated and VIRMOS-DESCART data

Free access article

Issue		A&A Volume 393, Number 2, October II 2002


Page(s)		369 - 379
Section		Cosmology
DOI		http://dx.doi.org/10.1051/0004-6361:20020932

A&A 393, 369-379 (2002)
DOI: 10.1051/0004-6361:20020932

Likelihood analysis of cosmic shear on simulated and VIRMOS-DESCART data

L. Van Waerbeke^{1, 2}, Y. Mellier^{1, 3}, R. Pelló⁴, U.-L. Pen², H. J. McCracken^{5, 6, 7} and B. Jain⁸

¹ Institut d'Astrophysique de Paris, 98 bis boulevard Arago, 75014 Paris, France
² Canadian Institute for Theoretical Astrophysics, 60 St George Str., Toronto, M5S 3H8, Canada
³ Observatoire de Paris, LERMA, 61 avenue de l'Observatoire, 75014 Paris, France
⁴ Observatoire Midi-Pyrénées, UMR 5572, 14 avenue E. Belin, 31400 Toulouse, France
⁵ Department of Astronomy, University of Bologna, via Ranzani 1, 40127 Bologna, Italy
⁶ Observatorio Astronomico di Bologna, via Ranzani 1, 40127 Bologna, Italy
⁷ Laboratoire d'Astrophysique de Marseille, Traverse du Siphon, 13376 Marseille Cedex 12, France
⁸ Department of Physics and Astronomy, University of Pennsylvania, 209 S. 33rd Street, Philadelphia, PA 19104, USA

(Received 28 February 2002 / Accepted 4 June 2002 )

Abstract
We present a maximum likelihood analysis of cosmological parameters from measurements of the aperture mass up to 35 arcmin using simulated and real cosmic shear data. A four-dimensional parameter space is explored which examines the mean density $\Omega_{\rm M}$ , the mass power spectrum normalisation $\sigma_8$ , the shape parameter $\Gamma$ and the redshift of the sources $z_{\rm s}$ . Constraints on $\Omega_{\rm M}$ and $\sigma_8$ (resp. $\Gamma$ and $z_{\rm s}$ ) are provided by marginalising over $\Gamma$ and $z_{\rm s}$ ( resp. $\Omega_{\rm M}$ and $\sigma_8$ ). For a flat $\Lambda$ CDM cosmologies, using a photometric redshift prior for the sources and $\Gamma \in [0.1,0.4]$ , we find $\sigma_8=\left(0.57\pm0.04\right) \Omega_{\rm M}^{\left(0.24\mp 0.18\right) \Omega_{\rm M}-0.49}$ at the $68\%$ confidence level (the error budget includes statistical noise, full cosmic variance and residual systematics). The estimate of $\Gamma$ , marginalised over $\Omega_{\rm M} \in [0.1,0.4]$ , $\sigma_8 \in [0.7,1.3]$ and $z_{\rm s}$ constrained by photometric redshifts, gives $\Gamma=0.25\pm 0.13$ at $68\%$ confidence. Adopting h=0.7, a flat universe, $\Gamma=0.2$ and $\Omega_{\rm m}=0.3$ we find $\sigma_8=0.98 \pm0.06$ . Combined with CMB measurements, our results suggest a non-zero cosmological constant and provide tight constraints on $\Omega_{\rm M}$ and $\sigma_8$ . Finally, we compare our results to the cluster abundance ones, and discuss the possible discrepancy with the latest determinations of the cluster method. In particular we point out the actual limitations of the mass power spectrum prediction in the non-linear regime, and the importance in improving this.

Key words: cosmology: dark matter -- cosmology: gravitational lensing

Offprint request: L. Van Waerbeke, waerbeke@iap.fr

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