Evolution of the Deterministic Collapse Barrier of the Field Clusters as a Probe of Cosmology

The collapse barrier, $δ_{c}$, of the field clusters located in the low-density environment is deterministic rather than diffusive, unlike that of the wall counterparts located in the superclusters. Analyzing the data from the Mira-Titan simulations for eleven different cosmologies including the standard $Λ$CDM cosmology at various redshifts, we investigate the evolution of the deterministic collapse barrier of the field clusters and explore its dependence on the background cosmology. Regardless of the background cosmology, the deterministic $δ_{c}$ exhibits a universal behavior of having a higher value than the Einstein-de Sitter spherical collapse barrier height of $δ_{sc}=1.686$, at $z=0$ but gradually converging down to $δ_{sc}$ as the dominance of dark energy diminishes with the increment of $z$. A significant difference among different cosmologies, however, is found in its convergence rate as well as in the critical redshift $z_{c}$ at which $δ_{c}=δ_{sc}$. Showing that the convergence rate and critical redshifts can distinguish even between the degenerate cosmologies which yield almost identical linear growth factor and cluster mass functions, we suggest that the evolution of the deterministic collapse barrier of the field clusters should be a powerful complementary probe of cosmology.