Cosmological constraints from the redshift dependence of the
  Alcock-Paczynski test and volume effect: galaxy two-point correlation
  function
  We propose a method using the redshift dependence of the Alcock-Paczynski
(AP) test and volume effect to measure the cosmic expansion history. The galaxy
two-point correlation function as a function of angle, $\xi(\mu)$, is measured
at different redshifts. Assuming an incorrect cosmological model to convert
galaxy redshifts to distances, the shape of $\xi(\mu)$ appears anisotropic due
to the AP effect, and the amplitude shifted by the change in comoving volume.
Due to the redshift dependence of the AP and volume effect, both the shape and
amplitude of $\xi(\mu)$ exhibit redshift dependence. Similar to Li et.al
(2014), we find the redshift-space distortions (RSD) caused by galaxy peculiar
velocities, although significantly distorts $\xi(\mu)$, exhibit much less
redshift evolution compared to the AP and volume effects. By focusing on the
redshift dependence of $\xi(\mu)$, we can correctly recover the cosmological
parameters despite the contamination of RSD. The method is tested by using the
Horizon Run 3 N-body simulation, from which we made a series of $1/8$-sky mock
surveys having 8 million physically self-bound halos and sampled to have
roughly a uniform number density in $z=0-1.5$. We find the AP effect results in
tight, unbiased constraints on the density parameter and dark energy equation
of state, with 68.3% CL intervals $\delta \Omega_m\sim0.03$ and $\delta
w\sim0.1$, and the volume effect leads to much tighter constraints of $\delta
\Omega_m\sim0.007$ and $\delta w\sim0.035$.
