  The major theoretical limitation for extracting cosmological parameters from
the CMB sky lies in the precision with which we can calculate the cosmological
recombination process. Uncertainty in the details of hydrogen and helium
recombination could effectively increase the errors or bias the values of the
cosmological parameters derived from the Planck satellite, for example. Here we
modify the cosmological recombination code RECFAST by introducing one more
parameter to reproduce the recent numerical results for the speed-up of the
helium recombination. Together with the existing hydrogen fudge factor, we vary
these two parameters to account for the remaining dominant uncertainties in
cosmological recombination. By using the CosmoMC code with Planck forecast
data, we find that we need to determine the parameters to better than ten per
cent for He I and one per cent for H, in order to obtain negligible effects on
the cosmological parameters. For helium recombination, if the existing studies
have calculated the ionization fraction to the 0.1 per cent level by properly
including the relevant physical processes, then we already have numerical
calculations which are accurate enough for Planck. For hydrogen, setting the
fudge factor to speed up low redshift recombination by 14 per cent appears to
be sufficient for Planck. However, more work still needs to be done to carry
out comprehensive numerical calculations of all the relevant effects for
hydrogen, as well as to check for effects which couple hydrogen and helium
recombinaton through the radiation field.
