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

Understand

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.