Regge calculus models of the closed vacuum $\Lambda$-FLRW universe
  The Collins-Williams Regge calculus models of FLRW space-times and Brewin's
subdivided models are applied to closed vacuum $\Lambda$-FLRW universes. In
each case, we embed the Regge Cauchy surfaces into 3-spheres in $\mathbf{E}^4$
and consider possible measures of Cauchy surface radius that can be derived
from the embedding. Regge equations are obtained from both global variation,
where entire sets of identical edges get varied simultaneously, and local
variation, where each edge gets varied individually. We explore the
relationship between the two sets of solutions, the conditions under which the
Regge Hamiltonian constraint would be a first integral of the evolution
equation, the initial value equation for each model at its moment of time
symmetry, and the performance of the various models. It is revealed that local
variation does not generally lead to a viable Regge model. It is also
demonstrated that the various models do satisfy their respective initial value
equations. Finally, it is shown that the models reproduce the behaviour of the
continuum model rather well initially, with performance improving as we
increase the number of tetrahedra used to construct the Regge Cauchy surface.
Eventually though, all models gradually fail to keep up with the continuum FLRW
model's expansion, with the models with lower numbers of tetrahedra falling
away more quickly. We believe this failure to keep up is due to the finite
resolution of the Regge Cauchy surfaces trying to approximate an ever expanding
continuum Cauchy surface; each Regge surface has a fixed number of tetrahedra
and as the surface being approximated gets larger, the resolution would
degrade. Finally, we note that all Regge models end abruptly at a point when
the time-like struts of the skeleton become null, though this end-point appears
to get delayed as the number of tetrahedra is increased.
