Manifold Properties from Causal Sets using Chains

Abstract

We study the utility of chains defined on causal sets in estimating continuum properties like the curvature, the proper time and the spacetime dimension through a numerical analysis. In particular, we show that in ${\text{dS}}_2$ and ${\text{FLRW}}_3$ spacetimes the formalism of arXiv:1212.0631 with slight modifications gives the right continuum properties. We also discuss a possible test of manifoldlikeness using this formalism by considering two models of non-manifoldlike causal sets. This is a part of a broader idea of the geometrical reconstruction of continuum properties given a discrete sub structure, in this case the causal set.

30 pages, 12 figures