Cosmological parameter determination from Planck and SDSS data in LambdaCHDM cosmologies

We study the complementarity between the cosmological information obtainable with the Planck surveyour and the large scale structure (LSS) redshift surveys in LambdaCHDM cosmologies. We compute the initial full phase-space neutrino distribution function for LambdaCHDM models by using numerical simulations. As initial condition we adopt the HDM density fluctuation power spectrum normalized on the basis of the analysis of the local cluster X-ray temperature function and derive the initial neutrino phase-space distribution at each spatial wave number k by using the Zel'dovich approximation. These initial neutrino phase-space distributions are implemented in the CMBFAST code for the integration of the coupled linearized Einstein, Boltzmann and fluid equations in k-space. We find that the relative bias between the CMB temperature fluctuations and the underlying matter density fluctuation power spectrum in COBE/DMR normalization is given by the CDM component normalized accordingly to the abundance of rich clusters at the present time. We use the Fisher information matrix approximation to constrain a multi-dimensional parametrization of the LambdaCHDM model, by jointly considering CMB and large scale structure data according to the Planck and the SDSS experimental specifications and by taking into account redshift distortions and nonlinear effects on the matter power spectrum. We found that, although the CMB anisotropy and polarization measurements tend to dominate the constraints on most of the cosmological parameters, the additional small scale LSS data help to break the parameter degeneracies. This work has been done in the framework of the Planck LFI activities.