Evolution of the Deterministic Collapse Barrier of the Field Clusters as
  a Probe of Cosmology
  The collapse barrier, $\delta_{c}$, 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
$\Lambda$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 $\delta_{c}$ exhibits a universal behavior of having a higher
value than the Einstein-de Sitter spherical collapse barrier height of
$\delta_{sc}=1.686$, at $z=0$ but gradually converging down to $\delta_{sc}$ 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
$\delta_{c}=\delta_{sc}$. 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.
