Standard Clustering Analysis: to obtain covariance, we need fast mock generation.
Models need very large and accurate simulations to calibrate.
Covariance needs relatively smaller simulations (the volume of the simulation should be simalar to the volume of the surveys to estimate the cosmic variance), less accurate but numerous, so fast approximate methods are needed.
Take N-body simulation as a reference, current fast methods (2LPT, and its modifications) provide matter field more and more accurately.
Modeling bias: based on the DM density field, use an effective bias model to approximate the Halo finder + Halo occupation model. -> generate mock galaxy catalogs fastly.
Sub-Halo Abundance Match(SHAM)
Field Level Model of Bias: local terms and non-local terms. (改进:EFT可以一次性写出所有的operators,而不是用到了再加)
Two mock generators used in BOSS and DESI:
PATCHY: eALPTvc matter ps 在 k<=0.2Mpc/h 的数据都比较准确。
EZmock: 1LPT (or Zel'dovich apporximation), matter ps 不太准,但通过 galaxy number PDF 校准后可以得到准确的 ps 和 bs.
Holi-mock: EZmock + cosmic web classification ——根据 Tidal field ∂ijϕ (和 ∂ijδ )的特征值,将 halo 所处的环境分为 filament, sheet, void, knot 四类(4x4=16类),分别做 PDF matching ,得到更好的 ps 和 bs.