A combined analysis of 3D weak lensing, Lyman-α forest and WMAP year three data

We present constraints on the amplitude and shape of the matter power spectrum and the density of dark matter within the framework of a standard Lambda CDM model. We use a Markov chain Monte Carlo approach to combine independent measurements of the three-dimensional weak gravitational lensing shear field by the COSMOS survey, of low- and high-resolution Lyman-alpha (Ly alpha) forest flux power spectrum by SDSS and LUQAS, and of cosmic microwave background temperature and polarization anisotropies by WMAP. We note good agreement between the amplitude of the matter power spectrum on intermediate and small scales as inferred from Lya forest and lensing data. The Lya forest data help to break the sigma(8)-Omega(0m) degeneracy characteristic of weak lensing results, yielding sigma 8 = 0.876 +/- 0.048 for COSMOS plus Lya SDSS data. This is somewhat larger than the value preferred by the WMAP year three CMB data. Combining all three data sets significantly tightens the constraints on sigma 8, the spectral index of primordial density fluctuation n(s), a possible running of the spectral index n(run) and the matter density Omega(0m). Assuming no running, the joint constraints for COSMOS, SDSS and WMAP are sigma 8 = 0.800 +/- 0.023, n(s) = 0.971 +/- 0.011, Omega(0m) = 0.247 +/- 0.016 ( 1-sigma error bars).