We apply the Velocity Distribution Function (VDF) to a sample of Sunyaev-Zeldovich (SZ)-selected clusters, and we report preliminary cosmological constraints in the $sigma_8$-$Omega_m$ cosmological parameter space. The VDF is a forward-modeled test statistic that can be used to constrain cosmological models directly from galaxy cluster dynamical observations. The method was introduced in Ntampaka et al. (2017) and employs line-of-sight velocity measurements to directly constrain cosmological parameters; it is less sensitive to measurement error than a standard halo mass function approach. The method is applied to the Hectospec Survey of Sunyaev-Zeldovich-Selected Clusters (HeCS-SZ) sample, which is a spectroscopic follow up of a Planck-selected sample of 83 galaxy clusters. Credible regions are calculated by comparing the VDF of the observed cluster sample to that of mock observations, yielding $mathcal{S}_8 equiv sigma_8 left(Omega_m/0.3right)^{0.25} = 0.751pm0.037$. These constraints are in tension with the Planck Cosmic Microwave Background (CMB) TT fiducial value, which lies outside of our 95% credible region, but are in agreement with some recent analyses of large scale structure that observe fewer massive clusters than are predicted by the Planck fiducial cosmological parameters.
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