Cosmological Constraints from the Redshift Dependence of the Alcock-Paczynski Effect: Possibility of Estimating the Nonlinear Systematics Using Fast Simulations

The tomographic Alcock-Paczynski (AP) method is so far the best method in separating the AP signal from the redshift space distortion (RSD) effects and deriving powerful constraints on cosmological parameters using the $\lesssim 40\,{h}^{-1}\ \mathrm{Mpc}$ ≲ 40 h - 1 Mpc clustering region. To guarantee that the method can be easily applied to the future large-scale structure surveys, we study the possibility of estimating the systematics of the method using the fast simulation method. The major contribution of the systematics comes from the nonzero redshift evolution of the RSD effects, which is quantified by ${\hat{\XI }}_{{\rm{\Delta }}s}(\mu ,z)$ ξ ̂ Δ s ( μ , z ) in our analysis, and estimated using the BigMultidark exact N-body simulation and approximate COmoving Lagrangian Acceleration (COLA) simulation samples. We find about 5%/10% evolution when comparing the ${\hat{\XI }}_{{\rm{\Delta }}s}(\mu ,z)$ ξ ̂ Δ s ( μ , 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 ≲1.5% change in ${\hat{\XI }}_{{\rm{\Delta }}s}$ ξ ̂ Δ s when varying the halo mass within the range of 2 × 10¹²-10¹⁴ M_⊙. We will perform more studies to achieve an accurate and efficient estimation of the systematics in the redshift range of z = 0-1.5.