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We present a prospective analysis of a combined cosmic shear and cosmicmicrowave background data set, focusing on a Canada France Hawaii TelescopeLegacy Survey (CFHTLS) type lensing survey and the current WMAP-1 year and CBIdata. We investigate the parameter degeneracies and error estimates of a sevenparameters model, for the lensing alone as well as for the combinedexperiments. The analysis is performed using a Monte Carlo Markov Chaincalculation, allowing for a more realistic estimate of errors and degeneraciesthan a Fisher matrix approach. After a detailed discussion of the relevantstatistical techniques, the set of the most relevant 2 and 3-dimensionallensing contours are given. It is shown that the combined cosmic shear and CMBis particularly efficient to break some parameter degeneracies. The principalcomponents directions are computed and it is found that the most orthogonalcontours 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 theprimordial mass power spectrum and the running spectral index respectively. Itis shown that an improvement of a factor 2 is expected on the running spectralindex from the combined data sets. Forecasts for error improvements from a widefield space telescope lensing survey are also given.Comment: 16 pages, 11 figures. Submitted to Astronomy & Astrophysic

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