How well do we understand cosmological recombination?

The major theoretical limitation for extracting cosmological parameters from the cosmic microwave background (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 10 per cent for He I and 1 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 recombination through the radiation field.