Cosmology with Galaxy Cluster Phase Spaces

We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in the redshift range $0 \leq z \leq 0.8$, after applying a conservative $80\%$ mass scatter prior on each cluster and marginalizing over all other parameters, we forecast $1\sigma$ constraints on the dark energy equation of state $w$ and matter density parameter $\Omega_M$ of $\sigma_w = 0.138 (0.431)$ and $\sigma_{\Omega_M} = 0.007 (0.025)$ in a flat universe. Assuming 40\% mass scatter and adding a prior on the Hubble constant we can achieve a constraint on the CPL parametrization of the dark energy equation of state parameters $w_0$ and $w_a$ with 100 clusters in the same redshift range: $\sigma_{w_0} = 0.191$ and $\sigma_{w_a} = 2.712$. Dropping the assumption of flatness and assuming $w=-1$ we also attain competitive constraints on the matter and dark energy density parameters: $\sigma_{\Omega_M} = 0.101$ and $\sigma_{\Omega_{\Lambda}} = 0.197$ for 100 clusters uniformly distributed in the range $0 \leq z \leq 0.8$ after applying a prior on the Hubble constant. We also discuss various observational strategies for tightening constraints in both the near and far future.