Reconstructing the recombination history by combining early and late cosmological probes

We develop and apply a new framework for reconstructing the ionization history during the epoch of recombination with combinations of cosmic microwave background (CMB), baryon acoustic oscillation (BAO) and supernova data. We find a wide range of ionization histories that are consistent with current CMB data, and also that cosmological parameter constraints are significantly weakened once freedom in recombination is introduced. BAO data partially break the degeneracy between cosmological parameters and the recombination model, and are therefore important in these reconstructions. The 95 on H0 are 80.1 (70.7) km/s/Mpc given CMB (CMB+BAO) data, assuming no other changes are made to the standard cosmological model. Including Cepheid-calibrated supernova data in the analysis drives a preference for non-standard recombination histories with visibility functions that peak early and exhibit appreciable skewness. Forthcoming measurements from SPT-3G will reduce the uncertainties in our reconstructions by about a factor of two.