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 Mpc/h. 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 - 100 Mpc/h. 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 BOSS survey should be able to detect gravitational redshifts from
large-scale structure at the ~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 percent 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.
