# Cluster Cosmology with the Velocity Distribution Function of the HeCS-SZ Sample

## TL;DR

This paper uses the Velocity Distribution Function of galaxy clusters from the HeCS-SZ sample to derive cosmological constraints, providing an alternative to traditional methods and highlighting tensions with Planck CMB results.

## Contribution

It introduces the application of the VDF method to SZ-selected clusters for cosmological constraints, demonstrating its effectiveness and potential discrepancies with Planck results.

## Key findings

- Derived _ = 0.751 b1 0.037 for _ = _(_m/0.3)^{0.25}
- Constraints are in tension with Planck CMB fiducial values
- Method shows promise for direct cosmological parameter estimation from dynamical observations

## Abstract

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.