Redshift weights for baryon acoustic oscillations: application to mock galaxy catalogues

Large redshift surveys capable of measuring the baryon acoustic oscillation (BAO) signal have proven to be an effective way of measuring the distance–redshift relation in cosmology. Building off the work in Zhu et al., we develop a technique to directly constrain the distance–redshift relation from BAO measurements without splitting the sample into redshift bins. We apply the redshift weighting technique in Zhu et al. to the clustering of galaxies from 1000 Quick particle mesh (QPM) mock simulations after reconstruction and achieve a 0.75 per cent measurement of the angular diameter distance DA at z = 0.64 and the same precision for Hubble parameter H at z = 0.29. These QPM mock catalogues mimic the clustering and noise level of the Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12). We compress the correlation functions in the redshift direction on to a set of weighted correlation functions. These estimators give unbiased DA and H measurements across the entire redshift range of the combined sample. We demonstrate the effectiveness of redshift weighting in improving the distance and Hubble parameter estimates. Instead of measuring at a single ‘effective’ redshift as in traditional analyses, we report our DA and H measurements at all redshifts. The measured fractional error of DA ranges from 1.53 per cent at z = 0.2 to 0.75 per cent at z = 0.64. The fractional error of H ranges from 0.75 per cent at z = 0.29 to 2.45 per cent at z = 0.7. Our measurements are consistent with a Fisher forecast to within 10–20 per cent depending on the pivot redshift. We further show the results are robust against the choice of fiducial cosmologies, galaxy bias models, and redshift–space distortions streaming parameters.