Spacetime Foam and the Cosmological Constant

TL;DR

This paper explores how the divergence in the sum over topologies in quantum gravity, related to the cosmological constant, suggests a mechanism for the cosmological constant to naturally approach zero.

Contribution

It proposes a thermodynamic analogy for quantum gravity path integrals, linking topology density growth to the cosmological constant's behavior.

Findings

Density of topologies grows superexponentially for negative b4

Sum over topologies diverges, indicating a maximum effective temperature

Effective cosmological constant may be driven to zero due to topology proliferation

Abstract

In the saddle point approximation, the Euclidean path integral for quantum gravity closely resembles a thermodynamic partition function, with the cosmological constant $\Lambda$ playing the role of temperature and the ``density of topologies'' acting as an effective density of states. For $\Lambda<0$, the density of topologies grows superexponentially, and the sum over topologies diverges. In thermodynamics, such a divergence can signal the existence of a maximum temperature. The same may be true in quantum gravity: the effective cosmological constant may be driven to zero by a rapid rise in the density of topologies.