Cosmology on Simplicial Complexes

Analytical solutions of the Einstein field equations heavily rely on symmetries imposed on the underlying spacetime. Due to the complexity of these non-linear coupled partial differential equations, finding more general solutions is a difficult task. In cosmology the most considerations are based on the well known FLRW metric or on perturbations of the latter, although the observed universe departs greatly from the underlying assumptions on smaller scales.

To address this issues, the framework of Regge calculus and its possible use for cosmology is examined. In this formalism the spacetime is approximated by finite sized simplices, building a simplicial complex and upon it a numerical time evolution scheme can be constructed. An introduction to the concepts in this field is presented together with an original method to account for the dynamical effects of the cosmological constant $\Lambda$. A new numerical library is briefly described. Finally, as an application, it is shown that the time evolution of the Kasner and $\Lambda$-vacuum spacetime can be reproduced.