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We present constraints on the amplitude and shape of the matter powerspectrum and the density of dark matter within the framework of a standardLambdaCDM model. We use a Markov Chain Monte Carlo approach to combineindependent measurements of the three dimensional weak gravitational lensingshear field by the COSMOS survey, of low and high resolution Ly-alpha forestflux power spectrum by SDSS and LUQAS, and of Cosmic Microwave Backgroundtemperature and polarization anisotropies by WMAP. We note good agreementbetween the amplitude of the matter power spectrum on intermediate and smallscales as inferred from Ly-alpha forest and lensing data. The Ly-alpha forestdata helps to break the sigma_8-Omega_m degeneracy characteristic of weaklensing results, yielding sigma_8 = 0.876 +- 0.048 for COSMOS plus Ly-alphaSDSS data. This is somewhat larger than the value preferred by the WMAP yearthree CMB data. Combining all three data sets significantly tightens theconstraints on sigma_8, the spectral index of primordial density fluctuationn_s, a possible running of the spectral index n_run and the matter densityOmega_m. Assuming no running, the joint constraints for COSMOS, SDSS and WMAPare sigma_8 = 0.800 +- 0.023, n_s = 0.971 +- 0.011, Omega_m = 0.247 +- 0.016(1-sigma error bars).

A combined analysis of 3D Weak Lensing, Lyman-alpha forest and WMAP year three data