Alcock-Paczynski Test with the Evolution of Redshift-Space Galaxy
  Clustering Anisotropy
  We develop an improved Alcock-Paczynski (AP) test method that uses the
redshift-space two-point correlation function (2pCF) of galaxies. Cosmological
constraints can be obtained by examining the redshift dependence of the
normalized 2pCF, which should not change apart from the expected small
non-linear evolution. An incorrect choice of cosmology used to convert redshift
to comoving distance will manifest itself as redshift-dependent 2pCF. Our
method decomposes the redshift difference of the two-dimensional correlation
function into the Legendre polynomials whose amplitudes are modeled by radial
fitting functions. Our likelihood analysis with this 2-D fitting scheme
tightens the constraints on $\Omega_m$ and ${w}$ by $\sim 40\%$ compared to the
method of Li et al. (2016, 2017, 2018) that uses one dimensional angular
dependence only. We also find that the correction for the non-linear evolution
in the 2pCF has a non-negligible cosmology dependence, which has been neglected
in previous similar studies by Li et al.. With an accurate accounting for the
non-linear systematics and use of full two-dimensional shape information of the
2pCF down to scales as small as $5~h^{-1}{\rm Mpc}$ it is expected that the AP
test with redshift-space galaxy clustering anisotropy can be a powerful method
to constrain the expansion history of the universe.
