Constraints on Omega_m and sigma_8 from weak lensing in RCS fields

We have analysed 53 square degrees of imaging data from the Red-Sequence Cluster Survey (RCS), and measured the excess correlations in the shapes of galaxies on scales out to ~1.5 degrees. We separate the signal into an E''- (lensing) and B’‘-mode (systematics), which allows us to study residual systematics. On scales larger than 10 arcminutes, we find no B''-mode. On smaller scales we find a small, but significant B’‘-mode. This signal is also present when we select a sample of bright galaxies. These galaxies are rather insensitive to observational distortions, and we therefore conclude that the oberved ``B’'-mode is likely to be caused by intrinsic alignments. We therefore 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. We obtain a conservative constraint of ${\sigma }_8=0.45_{-0.12}^{+0.09}{\mathrm{\Omega }}_m^{-0.55}$ (95% confidence). A better constraint is derived when we use Gaussian priors redshift distribution. For this choice of priors, we find ${\sigma }_8=(0.46_{-0.07}^{+0.05}){\mathrm{\Omega }}_m^{-0.52}$ (95% confidence). Using our setof Gaussian priors, we find that we can place a lower bound on Gamma: Gamma>0.1+0.16\Omega_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. (abridged)