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 $\delta w\sim0.035$.