Discrete gravity and and its continuum limit

TL;DR

This paper investigates the continuum limit of a discrete quantum gravity approach, showing that replacing a scalar field with Chaplygin gas allows for a well-defined continuum limit, implying a variable cosmological constant.

Contribution

It demonstrates that using Chaplygin gas instead of a massless scalar field enables the continuum limit in discrete quantum gravity models, suggesting a dynamic cosmological constant.

Findings

Continuum limit is achievable with Chaplygin gas.

Massless scalar field models require fine tuning for the continuum limit.

Replacing scalar fields with Chaplygin gas supports a variable cosmological constant.

Abstract

Recently Gambini and Pullin proposed a new consistent discrete approach to quantum gravity and applied it to cosmological models. One remarkable result of this approach is that the cosmological singularity can be avoided in a general fashion. However, whether the continuum limit of such discretized theories exists is model dependent. In the case of massless scalar field coupled to gravity with $\Lambda=0$, the continuum limit can only be achieved by fine tuning the recurrence constant. We regard this failure as the implication that cosmological constant should vary with time. For this reason we replace the massless scalar field by Chaplygin gas which may contribute an effective cosmological constant term with the evolution of the universe. It turns out that the continuum limit can be reached in this case indeed.