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We propose a method using the redshift dependence of the Alcock-Paczynski(AP) test and volume effect to measure the cosmic expansion history. The galaxytwo-point correlation function as a function of angle, $\xi(\mu)$, is measuredat different redshifts. Assuming an incorrect cosmological model to convertgalaxy redshifts to distances, the shape of $\xi(\mu)$ appears anisotropic dueto 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 andamplitude of $\xi(\mu)$ exhibit redshift dependence. Similar to Li et.al(2014), we find the redshift-space distortions (RSD) caused by galaxy peculiarvelocities, although significantly distorts $\xi(\mu)$, exhibit much lessredshift evolution compared to the AP and volume effects. By focusing on theredshift dependence of $\xi(\mu)$, we can correctly recover the cosmologicalparameters despite the contamination of RSD. The method is tested by using theHorizon Run 3 N-body simulation, from which we made a series of $1/8$-sky mocksurveys having 8 million physically self-bound halos and sampled to haveroughly a uniform number density in $z=0-1.5$. We find the AP effect results intight, unbiased constraints on the density parameter and dark energy equationof state, with 68.3% CL intervals $\delta \Omega_m\sim0.03$ and $\deltaw\sim0.1$, and the volume effect leads to much tighter constraints of $\delta\Omega_m\sim0.007$ and $\delta w\sim0.035$.

Cosmological constraints from the redshift dependence of the Alcock-Paczynski test and volume effect: galaxy two-point correlation function