Cosmic shear results from the deep lens survey - I: Joint constraints on
  omega_m and sigma_8 with a two-dimensional analysis
  We present a cosmic shear study from the Deep Lens Survey (DLS), a deep BVRz
multi-band imaging survey of five 4 sq. degree fields with two National Optical
Astronomy Observatory (NOAO) 4-meter telescopes at Kitt Peak and Cerro Tololo.
For both telescopes, the change of the point-spread-function (PSF) shape across
the focal plane is complicated, and the exposure-to-exposure variation of this
position-dependent PSF change is significant. We overcome this challenge by
modeling the PSF separately for individual exposures and CCDs with principal
component analysis (PCA). We find that stacking these PSFs reproduces the final
PSF pattern on the mosaic image with high fidelity, and the method successfully
separates PSF-induced systematics from gravitational lensing effects. We
calibrate our shears and estimate the errors, utilizing an image simulator,
which generates sheared ground-based galaxy images from deep Hubble Space
Telescope archival data with a realistic atmospheric turbulence model. For
cosmological parameter constraints, we marginalize over shear calibration
error, photometric redshift uncertainty, and the Hubble constant. We use
cosmology-dependent covariances for the Markov Chain Monte Carlo analysis and
find that the role of this varying covariance is critical in our parameter
estimation. Our current non-tomographic analysis alone constrains the
Omega_M-sigma_8 likelihood contour tightly, providing a joint constraint of
Omega_M=0.262+-0.051 and sigma_8=0.868+-0.071. We expect that a future DLS
weak-lensing tomographic study will further tighten these constraints because
explicit treatment of the redshift dependence of cosmic shear more efficiently
breaks the Omega_M-sigma_8 degeneracy. Combining the current results with the
Wilkinson Microwave Anisotropy Probe 7-year (WMAP7) likelihood data, we obtain
Omega_M=0.278+-0.018 and sigma_8=0.815+-0.020.
