We study the two-point cross-correlation function between two populations of galaxies: for instance, a bright population and a faint population. We show that this cross-correlation is asymmetric under the exchange of the line-of-sight coordinate of the galaxies, i.e. that the correlation is different if the bright galaxy is in front of, or behind, the faint galaxy. We give an intuitive, quasi-Newtonian derivation of all the effects that contribute to such an asymmetry in large-scale structure: gravitational redshift, Doppler shift, lensing, light-cone, evolution and Alcock-Paczynski effects; interestingly, the gravitational redshift term is exactly canceled by some of the others, assuming geodesic motion. Most of these effects are captured by previous calculations of general relativistic corrections to the observed galaxy density fluctuation; the asymmetry arises from terms that are suppressed by the ratio ($\mathcal{H}/k$)—$\mathcal{H}$ is the Hubble constant and $k$ is the wave number—which are more readily observable than the terms suppressed by $(\mathcal{H}/k{)}^2$. Some of the contributions to the asymmetry, however, arise from terms that are generally considered “Newtonian”—the lensing and evolution—and thus represent a contaminant in the search for general relativistic corrections. We propose methods to disentangle these different contributions. A simple method reduces the contamination to a level of $\lesssim 10\%$ for redshifts $z\lesssim 1$. We also clarify the relation to recent work on measuring gravitational redshifts by stacking clusters.

• Received 10 September 2013

DOI:https://doi.org/10.1103/PhysRevD.89.083535