GaBoDS: The Garching-Bonn deep survey - VII. Cosmic shear analysis

Aims. We present a cosmic shear analysis and data validation of 15 square degree high-quality R-band data of the Garching-Bonn Deep Survey obtained with the Wide Field Imager of the MPG/ESO 2.2 m telescope. Methods. We measure the two-point shear correlation functions to calculate the aperture mass dispersion. Both statistics are used to perform the data quality control. Combining the cosmic shear signal with a photometric redshift distribution of a galaxy sub-sample obtained from two square degree of UBVRI-band observations of the Deep Public Survey we determine constraints for the matter density Omega(m), the mass power spectrum normalisation sigma(8) and the dark energy density Omega(Lambda) in the magnitude interval R is an element of [21.5, 24.5]. In this magnitude interval the effective number density of source galaxies is n = 12.5 arcmin(-2), and their mean redshift is (z) over bar = 0.78. To estimate the posterior likelihood we employ the Monte Carlo Markov Chain method. Results. Using the aperture mass dispersion we obtain for the mass power spectrum normalisation sigma(8) = 0.80 +/- 0.10 (1 sigma statistical error) at a fixed matter density Omega(m) = 0.30 assuming a flat universe with negligible baryon content and marginalising over the Hubble parameter and the uncertainties in the fitted redshift distribution.