  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.
