The velocity distribution function of galaxy clusters as a cosmological probe

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), $dn\left(M\right)/dlog\left(M\right)$, which is strongly affected by mass measurement errors. In our new method, the probability distributions of velocities for each cluster in the sample are summed to create a new statistic called the velocity distribution function (VDF), $dn\left(v\right)/dv$. The VDF can be measured more directly and precisely than the HMF and can be robustly predicted with cosmological simulations that 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 Ω_m and the amplitude of matter fluctuations σ₈ in flat ΛCDM cosmologies. For an example observation of 200 massive clusters, the VDF with (without) interloping galaxies constrains the parameter combination ${\sigma }_8{\Omega }_m^{0.29\left(0.29\right)}=0.589\pm 0.014(0.584\pm 0.011)$ and shows only minor bias. However, the HMF with interlopers is biased to low Ω_m and high σ₈ and the fiducial model lies well outside of the forecast constraints, prior to accounting for Eddington bias. When the VDF is combined with constraints from the cosmic microwave background, the degeneracy between cosmological parameters can be significantly reduced. Upcoming spectroscopic surveys that probe larger volumes and fainter magnitudes will provide clusters for applying the VDF as a cosmological probe.