Vol 21, No 7

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

Jun-De Chen, Peng-Jie Zhang, Yi Zheng


Abstract The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments \(\langle v_{12}^n\rangle\). Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants \(\langle v_{12}^n\rangle_c\). We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at \(k_{||} < 0.1~h\rm~ Mpc^{-1}\) , including only the n = 1, 2 cumulants is sufficient. (3) But for modeling RSD at \(k_{||} < 0.2~h\rm~ Mpc^{-1}\), we need and only need the n = 1, 2, 3, 4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.


Keywords cosmology — dark energy — dark matter — large-scale structure of universe

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