Cosmological modelling with Regge calculus
  The late universe's matter distribution obeys the Copernican principle at
only the coarsest of scales. The relative importance of such inhomogeneity is
still not well understood. Because of the Einstein field equations' non-linear
nature, some argue a non-perturbative approach is necessary to correctly model
inhomogeneities and may even obviate any need for dark energy. We shall discuss
an approach based on Regge calculus, a discrete approximation to general
relativity: we shall discuss the Collins--Williams formulation of Regge
calculus and its application to two toy universes. The first is a universe for
which the continuum solution is well-established, the $\Lambda$-FLRW universe.
The second is an inhomogeneous universe, the `lattice universe' wherein matter
consists solely of a lattice of point masses with pure vacuum in between, a
distribution more similar to that of the actual universe compared to FLRW
universes. We shall discuss both regular lattices and one where one mass gets
perturbed.
