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
It accepts original submissions from all over the world and is internationally published and distributed by IOP