Abstract

We present a new approach for quantifying the abundance of galaxy clusters and constraining cosmological parameters using dynamical measurements. In the standard method, galaxy line-of-sight velocities, $v$ , or velocity dispersions are used to infer cluster masses, $M$ , to quantify the halo mass function (HMF), $dn(M)/d\log(M)$ , which is strongly affected by mass measurement errors. In our new method, the probability distribution of velocities for each cluster in the sample are summed to create a new statistic called the velocity distribution function (VDF), $dn(v)/dv$ . The VDF can be measured more directly and precisely than the HMF and can be robustly predicted with cosmological simulations which capture the dynamics of subhalos or galaxies. We apply these two methods to realistic (ideal) mock cluster catalogs with (without) interlopers and forecast the bias and constraints on the matter density parameter $\Omega_{m}$ and the amplitude of matter fluctuations $\sigma_{8}$ in flat $\Lambda$ CDM cosmologies. For an example observation of 200 massive clusters, the VDF with (without) interloping galaxies constrains the parameter combination $\smash{\sigma_{8}\,\Omega_{m}^{0.29\ (0