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 deg2 RC-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 θap = 2′ and 40'. We also detect a small but nonzero B-mode variance on scales larger than θap > 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 σ8, Ωm, Γ (the shape parameter of the CDM power spectrum), and 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 Γ < 0.5 for s > 0.9 (68% confidence). For a prior Γ ∈ [0.1, 0.4] and s ∈ [0.6, 1.4], we find σ8 = (0.50)Ω for Ωm + ΩΛ = 1 and σ8 = (0.51)Ω for ΩΛ = 0 (95% confidence). If we take the currently popular ΛCDM model (Ωm = 0.3, Ωλ = 0.7, Γ = 0.21), we obtain a one-dimensional confidence interval on σ8 for the 95.4% level, 0.62 < σ8 < 1.32 for s ∈ [0.6, 1.4]. Information on the redshift distribution of galaxies is key to obtaining a correct cosmological constraint. An independent constraint on Γ from other observations is useful to tighten the constraint.