Gravitational redshifts from large-scale structure

The recent measurement of the gravitational redshifts of galaxies in galaxy clusters by Wojtak et al. has opened a new observational window on dark matter and modified gravity. By stacking clusters this determination effectively used the line-of-sight distortion of the cross-correlation function of massive galaxies and lower mass galaxies to estimate the gravitational redshift profile of clusters out to 4 h(-1) Mpc. Here we use a halo model of clustering to predict the distortion due to gravitational redshifts of the cross-correlation function on scales from 1 to 100 h(-1) Mpc. We compare our predictions to simulations and use the simulations to make mock catalogues relevant to current and future galaxy redshift surveys. Without formulating an optimal estimator, we find that the full Baryonic Oscillation Spectroscopic Survey (BOSS) survey should be able to detect gravitational redshifts from large-scale structure at the similar to 4 Sigma level. Upcoming redshift surveys will greatly increase the number of galaxies useable in such studies and the BigBOSS and Euclid experiments should be capable of measurements with precision at the few per cent level. As has been recently pointed out by McDonald, Kaiser and Zhao et al., other interesting effects including relativistic beaming and transverse Doppler shift can add additional asymmetric distortions to the correlation function. While these contributions are subdominant to the gravitational redshift on large scales, they represent additional opportunities to probe gravitational physics and indicate that many qualitatively new measurements should soon be possible using large redshift surveys.