### On Escaping a Galaxy Cluster in an Accelerating Universe

(7 votes from 5 institutions)

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.