Estimating the impact of recombination uncertainties on the cosmological
  parameter constraints from cosmic microwave background experiments
  [Abridged] We use our most recent training set for the RICO code to estimate
the impact of recombination uncertainties on the posterior probability
distributions which will be obtained from future CMB experiments, and in
particular the Planck satellite. Using a MCMC analysis to sample the posterior
distribution of the cosmological parameters, we find that Planck will have
biases of -0.7, -0.3 and -0.4 sigmas for n_S, Omega_b h2 and log(As),
respectively, in the minimal 6-parameter LCDM model, if the description of the
recombination history given by RICO is not used. The remaining parameters are
not significantly affected. We also show, that the cosmology dependence of the
corrections to the recombination history modeled with RICO has a negligible
impact on the posterior distributions obtained for the case of the Planck
satellite. In practice, this implies that the inclusion of additional
corrections to existing recombination codes can be achieved using simple
cosmology-independent `fudge functions'. Finally, we also investigated the
impact of some recent improvements in the treatment of hydrogen recombination
which are still not included in the current version of our training set for
Rico, by assuming that the cosmology dependence of those corrections can be
neglected. In summary, with our current understanding of the complete
recombination process, the expected biases in the cosmological parameters
inferred from Planck might be as large as -2.3, -1.7 and -1 sigmas for n_S,
Omega_b h2 and log(As) respectively, if all those corrections are not taken
into account. We note that although the list of physical processes that could
be of importance for Planck seems to be nearly complete, still some effort has
to be put in the validation of the results obtained by the different groups.
