Cluster Cosmology with the Velocity Distribution Function of the HeCS-SZ
  Sample
  We apply the Velocity Distribution Function (VDF) to a sample of
Sunyaev-Zel'dovich (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 $\mathcal{S}_8 \equiv \sigma_8
\left(\Omega_m/0.3\right)^{0.25} = 0.751\pm0.037$. 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.
