Constraints on Ωm and σ8 from weak lensing in red-sequence cluster survey fields

We have analyzed 53 deg(2) of R(C)-band imaging data from the Red-Sequence Cluster Survey (RCS) and measured the excess correlations in the shapes of galaxies on scales out to similar to1.degrees5. We separate the signal into an "E" (lensing) and "B" ( systematics) mode, which allows us to study the contribution from residual systematics and intrinsic alignments. On scales larger than 10', we find no B mode, suggesting that the signal at those scales is caused solely by gravitational lensing. On smaller scales we find a small but significant B mode. This signal is also present when we select a sample of bright (20 < R(C) < 22) galaxies. These galaxies are rather insensitive to observational distortions, and we therefore conclude that the observed B mode is likely to be caused by intrinsic alignments. To minimize the effect of intrinsic alignments, we limit the cosmic shear analysis to galaxies with 22 < R(C) < 24. We derive joint constraints on Omega(m) and sigma(8) by marginalizing over Gamma, Omega(Lambda), and the source redshift distribution, using different priors. Marginalizing over Gamma and Omega(Lambda), and using a flat prior for the source redshift distribution, yields a conservative constraint of sigma(8) = 0.4(-0.12)(+0.09)Omega(m)(-0.55) (95% confidence). A better constraint is derived when we use Gaussian priors for Gamma (from the Two-Degree Field survey) and Omega(m) + Omega(Lambda) (from cosmic microwave background [CMB]), and the source redshift distribution. For this choice of priors, we find sigma(8) = (0.46(-0.07)(+0.05))Omega(m)(-0.52) (95% confidence). We also investigated whether the RCS data can be used to constrain Gamma. Using our set of Gaussian priors, we find that we can only place a lower bound on Gamma for which we find Gamma > 0.1 + 0.16Omega(m) (95% confidence). Comparison of the RCS results with three other recent cosmic shear measurements shows excellent agreement. The current weak-lensing results are also in good agreement with CMB measurements, when we allow the reionization optical depth tau and the spectral index n(s) to vary. We present a simple demonstration of how the weak-lensing results can be used as a prior in the parameter estimation from CMB measurements to derive constraints on the reionization optical depth tau.