Two cosmological solutions of Regge calculus

Abstract

Two cosmological solutions of Regge calculus are presented which correspond to the flat Friedmann-Robertson-Walker and the Kasner solutions of general relativity. By taking advantage of the symmetries that are present, I am able to show explicitly that a limit of Regge calculus does yield Einstein's equations for these cases. The method of averaging these equations when taking limits is important, especially for the Kasner model. I display the leading error term that arises from keeping the Regge equations in discrete form rather than using their continuum limit. In particular, this work shows that for the "Reggeized" Friedmann model the minimum volume is a velocitydominated singularity as in the continuum Friedmann model. However, unlike the latter, the Regge version has a nonzero minimum volume.