zBEAMS: A unified solution for supernova cosmology with redshift uncertainties

Supernova cosmology without spectra will be the bread and butter mode for future surveys such as LSST. This lack of supernova spectra results in uncertainty in the redshifts which, if ignored, leads to significantly biased estimates of cosmological parameters. Here we present a hierarchical Bayesian formalism -- zBEAMS -- that fully addresses this problem by marginalising over the unknown or contaminated supernova redshifts to produce unbiased cosmological estimates that are competitive with entirely spectroscopic data. zBEAMS provides a unified treatment of both photometric redshifts and host galaxy misidentification (occurring due to chance galaxy alignments or faint hosts), effectively correcting the inevitable contamination in the Hubble diagram. Like its predecessor BEAMS, our formalism also takes care of non-Ia supernova contamination by marginalising over the unknown supernova type. We demonstrate the effectiveness of this technique with simulations of supernovae with photometric redshifts and host galaxy misidentification. A novel feature of the photometric redshift case is the important role played by the redshift distribution of the supernovae.