We combine measurements of weak gravitational lensing from the CFHTLS-Wide survey, supernovae Ia from CFHT SNLS and CMB anisotropies from WMAP5 to obtain joint constraints on cosmological parameters, in particular, the dark energy equation of state p
arameter w. We assess the influence of systematics in the data on the results and look for possible correlations with cosmological parameters. We implement an MCMC algorithm to sample the parameter space of a flat CDM model with a dark-energy component of constant w. Systematics in the data are parametrised and included in the analysis. We determine the influence of photometric calibration of SNIa data on cosmological results by calculating the response of the distance modulus to photometric zero-point variations. The weak lensing data set is tested for anomalous field-to-field variations and a systematic shape measurement bias for high-z galaxies. Ignoring photometric uncertainties for SNLS biases cosmological parameters by at most 20% of the statistical errors, using supernovae only; the parameter uncertainties are underestimated by 10%. The weak lensing field-to-field variance pointings is 5%-15% higher than that predicted from N-body simulations. We find no bias of the lensing signal at high redshift, within the framework of a simple model. Assuming a systematic underestimation of the lensing signal at high redshift, the normalisation sigma_8 increases by up to 8%. Combining all three probes we obtain -0.10<1+w<0.06 at 68% confidence (-0.18<1+w<0.12 at 95%), including systematic errors. Systematics in the data increase the error bars by up to 35%; the best-fit values change by less than 0.15sigma. [Abridged]
We introduce an optimized data vector of cosmic shear measures (N). This data vector has high information content, is not sensitive against B-mode contamination and only shows small correlation between data points of different angular scales. We show
that a data vector of the two-point correlation function (2PCF) in general contains more information on cosmological parameters compared to a data vector of the aperture mass dispersion. Reason for this is the fact that <M_ap^2> lacks the information of the convergence power spectrum (P_kappa) on large angular scales, which is contained in the 2PCF data vector. Therefore we create a combined data vector N, which retains the advantages of <M_ap^2> and in addition is also sensitive to the large-scale information of P_kappa. We compare the information content of the three data vectors by performing a detailed likelihood analysis and use ray-tracing simulations to derive the covariance matrices. In the last part of the paper we contaminate all data vectors with B-modes on small angular scales and examine their robustness against this contamination.The combined data vector strongly improves constraints on cosmological parameters compared to <M_ap^2>. Although, in case of a pure E-mode signal the information content of the 2PCF is higher, in the more realistic case where B-modes are present the 2PCF data vector is strongly contaminated and yields biased cosmological parameter estimates. N shows to be robust against this contamination. Furthermore the individual data points of N show a much smaller correlation compared to the 2PCF leading to an almost diagonal covariance matrix.
