Title: Relativistic asymmetries in the galaxy cross-correlation function,
Abstract: We study the asymmetry in the two-point cross-correlation function of two
populations of galaxies focusing in particular on the relativistic effects that
include the gravitational redshift. We derive the cross-correlation function on
small and large scales using two different approaches: General Relativistic and
Newtonian perturbation theory. Following recent work by Bonvin et al.,
Gaztanaga et al. and Croft, we calculate the dipole and the shell estimator
with the two procedures and we compare our results. We find that while General
Relativistic Perturbation Theory (GRPT) is able to make predictions of
relativistic effects on very large, obviously linear scales (r > 50 Mpc/h), the
presence of non-linearities physically occurring on much smaller scales (down
to those describing galactic potential wells) can strongly affect the asymmetry
estimators. These can lead to cancellations of the relativistic terms, and sign
changes in the estimators on scales up to r ~ 50 Mpc/h. On the other hand, with
an appropriate non-linear gravitational potential, the results obtained using
Newtonian theory can successfully describe the asymmetry on smaller, non-linear
scales (r < 20 Mpc/h) where gravitational redshift is the dominant term. On
larger scales the asymmetry is much smaller in magnitude, and measurement is
not within reach of current observations. This is in agreement with the
observational results obtained by Gaztnaga et al. and the first detection of
relativistic effects (on (r < 20 Mpc/h) scales) by Alam et al.