On Escaping a Galaxy Cluster in an Accelerating Universe
  We derive the escape velocity profile for an Einasto density field in an
accelerating universe and demonstrate its physical viability by comparing
theoretical expectations to both light-cone data generated from N-body
simulations and archival data on 20 galaxy clusters. We demonstrate that the
projection function ($g(\beta )$) is deemed physically viable only for the
theoretical expectation that includes a cosmology-dependent term. Using
simulations, we show that the inferred velocity anisotropy is more than
6{\sigma} away from the expected value for the theoretical profile that ignores
the acceleration of the universe. In the archival data, we constrain the
average velocity anisotropy parameter of a sample of 20 clusters to be $\beta
={0.248}_{-0.360}^{+0.164}$ at the 68% confidence level. Lastly, we briefly
discuss how our analytic model may be used as a novel cosmological probe based
on galaxy clusters.
