  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.
