Cosmological Parameter Determination fromPlanckand Sloan Digital Sky Survey Data in Λ Cold+Hot Dark Matter Cosmologies

We study the complementarity between the cosmological information obtainablewith the Planck surveyour and the large scale structure (LSS) redshift surveysin LambdaCHDM cosmologies. We compute the initial full phase-space neutrinodistribution function for LambdaCHDM models by using numerical simulations. Asinitial condition we adopt the HDM density fluctuation power spectrumnormalized on the basis of the analysis of the local cluster X-ray temperaturefunction and derive the initial neutrino phase-space distribution at eachspatial wave number k by using the Zel'dovich approximation. These initialneutrino phase-space distributions are implemented in the CMBFAST code for theintegration of the coupled linearized Einstein, Boltzmann and fluid equationsin k-space. We find that the relative bias between the CMB temperaturefluctuations and the underlying matter density fluctuation power spectrum inCOBE/DMR normalization is given by the CDM component normalized accordingly tothe abundance of rich clusters at the present time. We use the Fisherinformation matrix approximation to constrain a multi-dimensionalparametrization of the LambdaCHDM model, by jointly considering CMB and largescale structure data according to the Planck and the SDSS experimentalspecifications and by taking into account redshift distortions and nonlineareffects on the matter power spectrum. We found that, although the CMBanisotropy and polarization measurements tend to dominate the constraints onmost of the cosmological parameters, the additional small scale LSS data helpto break the parameter degeneracies. This work has been done in the frameworkof the Planck LFI activities.Comment: 36 pages and 8 figures in AAS LATEX macros v5.0 (submitted to ApJ