Joint cosmological parameters forecast from CFHTLS-cosmic shear and CMB data

We present a prospective analysis of a combined cosmic shear and cosmic microwave background data set, focusing on a Canada France Hawaii Telescope Legacy Survey (CFHTLS) type lensing survey and the current WMAP-1 year and CBI data. We investigate the parameter degeneracies and error estimates of a seven parameters model, for the lensing alone as well as for the combined experiments. The analysis is performed using a Monte Carlo Markov Chain calculation, allowing for a more realistic estimate of errors and degeneracies than a Fisher matrix approach. After a detailed discussion of the relevant statistical techniques, the set of the most relevant 2 and 3-dimensional lensing contours are given. It is shown that the combined cosmic shear and CMB is particularly efficient to break some parameter degeneracies. The principal components directions are computed and it is found that the most orthogonal contours between the two experiments are for the parameter pairs (Omega_m,sigma_8), (h,ns) and (ns,nrun), where ns and nrun are the slope of the primordial mass power spectrum and the running spectral index respectively. It is shown that an improvement of a factor 2 is expected on the running spectral index from the combined data sets. Forecasts for error improvements from a wide field space telescope lensing survey are also given.