Cosmological constraints from the redshift dependence of the
  Alcock-Paczynski effect: Possibility of estimateing the non-linear
  systematics using fast simulations
  The tomographic AP method is so far the best method in separating the
Alcock-Paczynski (AP) signal from the redshift space distortion (RSD) effects
and deriving powerful constraints on cosmological parameters using the
$\lesssim40h^{-1}\ \rm Mpc$ clustering region. To guarantee that the method can
be easily applied to the future large scale structure (LSS) surveys, we study
the possibility of estimating the systematics of the method using fast
simulation method. The major contribution of the systematics comes from the
non-zero redshift evolution of the RSD effects, which is quantified by
$\hat\xi_{\Delta s}(\mu,z)$ in our analysis, and estimated using the
BigMultidark exact N-body simulation and approximate COLA simulation samples.
We find about 5\%/10\% evolution when comparing the $\hat\xi_{\Delta s}(\mu,z)$
measured as $z=0.5$/$z=1$ to the measurements at $z=0$. We checked the
inaccuracy in the 2pCFs computed using COLA, and find it 5-10 times smaller
than the intrinsic systematics of the tomographic AP method, indicating that
using COLA to estimate the systematics is good enough. Finally, we test the
effect of halo bias, and find $\lesssim$1.5\% change in $\hat\xi_{\Delta s}$
when varying the halo mass within the range of $2\times 10^{12}$ to $10^{14}$
$M_{\odot}$. We will perform more studies to achieve an accurate and efficient
estimation of the systematics in redshift range of $z=0-1.5$.
