Cosmic shear statistics in the Suprime-Cam 2.1 square degree field:: Constraints on Ωm and σ8

We present measurements of the cosmic shear correlation in the shapes of galaxies in the Suprime-Cam 2.1 deg(2) R-C-band imaging data. As an estimator of the shear correlation originating from the gravitational lensing, we adopt the aperture mass variance, which most naturally decomposes the correlation signal into E and B (non-gravitational lensing) modes. We detect a nonzero E mode variance on scales between theta(ap) = 2' and 40'. We also detect a small but nonzero B-mode variance on scales larger than theta(ap) > 5'. We compare the measured E-mode variance to the model predictions in CDM cosmologies using maximum likelihood analysis. A four-dimensional space is explored, which examines sigma(8), Omega(m), Gamma (the shape parameter of the CDM power spectrum), and (z) over bar (s) (mean redshift of galaxies). We include three possible sources of error: statistical noise, the cosmic variance estimated using numerical experiments, and a residual systematic effect estimated from the B-mode variance. We derive joint constraints on two parameters by marginalizing over the two remaining parameters. We obtain an upper limit of Gamma < 0.5 for <(z)over bar>(s) > 0.9 (68% confidence). For a prior Gamma is an element of [0,1, 0.4] and (z) over bar (s) [0.6, 1.4], we find sigma(8) = (0.50(-0.16)(+0.35) Omega(m)(-0.37) for Omega(m) + Omega(Lambda) = 1 and sigma(8) = (0.51(-0.16)(+0.29)) Omega(m)(-0.34) for Omega(Lambda) = 0 (95% confidence). If we take the currently popular LambdaCDM model (Omega(m) = 0.3, Omega(lambda) = 0.7, Gamma = 0.21), we obtain a one-dimensional confidence interval on sigma(8) for the 95.4% level, 0.62 < σ(8) < 1.32 for (z) over bar (s) is an element of [0.6; 1.4]. Information on the redshift distribution of galaxies is key to obtaining a correct cosmological constraint. An independent constraint on Gamma from other observations is useful to tighten the constraint.