星系红移巡天中的红移畸变效应是指由星系本动速度引起的，观测到红移空间中星系成团性呈现各向异性的效应。它是很重要的宇宙学探针，能够帮助我们重构宇宙结构形成的历史，结合宇宙膨胀历史的研究，我们可以打破暗能量模型和修正引力模型的简便性，更精确地限制宇宙学参数。随着观测精度的提高，下一代星系红移巡天(DESI, Euclid, LSST 等)有望将红移畸变效应测量的统计误差降低到1%左右，然而目前红移畸变模型普遍都还有5%∼10%的系统误差，因此，红移畸变模型的精度已经成为这个领域发展的瓶颈。我们介绍了几个主流的红移畸变模型，重点讨论每个模型中采用的假设及其局限性，并提出进一步改进的方向。%Redshift space distortion (RSD) in galaxy redshift survey is a very powerful cosmological probe, through which we could study the structure formation history of our universe. Combine the cosmological structure growth history with the expansion history, we could discriminate between different cosmological models, e.g. dark energy and modified gravity models. Currently many large galaxy redshift surveys, like 2dF, SDSS, VVDS, WiggleZ and BOSS, have measured the cosmological linear growth rate to the accuracy of about 5%. The stage IV dark energy projects like MS-DESI and Euclid have the ability to control the statistical error under 1%. It has become a bottleneck in the current RSD models that the systematic errors are still at 10%∼15%, much larger than the statistical errors of future galaxy redshift surveys. In this paper we review the current RSD models, discuss their (dis)advantages and ways to improve them. In particular, we choose three typical models to discuss and compare with each other, through which we discuss the key points in RSD cosmology and its future application. The main difficulty in modelling RSD effect lies on that this effect contains many non-linear procedures, respectively (1) the non-linear evolutions of the density and velocity field, (2) the non-linear mapping from real space to redshift space, (3) the complicated galaxy density bias and velocity bias problems. The key ingredient here is the mapping from real space to redshift space, for which we need to use perturbation theory to expand the redshift space density field using the real space density field. Different perturbation theories have their own advantages and disadvantages, and all of them become inaccurate at non-linear regime, so we should use simulations to test the available scales of the perturbation theories. During the test, we also find that there are no accurate enough perturbation theory for the real space density and velocity power spectra, so in order to make sure we clearly separate the previously mentioned (1) and (2) points, it is better to use the measured power spectra from simulation as input for the RSD models, and this is also an advantage of using simulations. As for the non-linear parts of RSD effect, in particular the FoG effect, the simulations also help us to find a physical and accurate fitting formula. In conclusion, modelling RSD effect is not just a simple mathematical expansion, but a derivation which needs many physically reasonable assumptions. It is particularly important to test every assumption separately utilizing simulations and make sure the modelling is carried out in the applicable scale for each assumption, then we could more efficiently search for better perturbation theory and FoG fitting formula and finally make the FoG cosmology more physical and accurate.
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