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The mapping of dark matter clustering from real space to redshift spaceintroduces the anisotropic property to the measured density power spectrum inredshift space, known as the redshift space distortion effect. The mappingformula is intrinsically non-linear, which is complicated by the higher orderpolynomials due to indefinite cross correlations between the density andvelocity fields, and the Finger-of-God effect due to the randomness of thepeculiar velocity field. Whilst the full higher order polynomials remainunknown, the other systematics can be controlled consistently within the sameorder truncation in the expansion of the mapping formula, as shown in thispaper. The systematic due to the unknown non-linear density and velocity fieldsis removed by separately measuring all terms in the expansion directly usingsimulations. The uncertainty caused by the velocity randomness is controlled bysplitting the FoG term into two pieces, 1) the "one-point" FoG term beingindependent of the separation vector between two different points, and 2) the"correlated" FoG term appearing as an indefinite polynomials which is expandedin the same order as all other perturbative polynomials. Using 100 realizationsof simulations, we find that the Gaussian FoG function with only onescale-independent free parameter works quite well, and that our new mappingformulation accurately reproduces the observed 2-dimensional density powerspectrum in redshift space at the smallest scales by far, up to $k\sim0.2h$Mpc, considering the resolution of future experiments.

Study on the mapping of dark matter clustering from real space to redshift space