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 $\mathrm{\Lambda }$-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.