Linking the Baum-Hawking-Coleman Mechanism with Unimodular Gravity and Vilenkin's Probability Flux

TL;DR

This paper explores a novel approach to the cosmological constant problem by linking the Baum-Hawking-Coleman mechanism with Unimodular Gravity and Vilenkin's probability flux, introducing new actions and interpretations.

Contribution

It introduces a new action coupling the four-form field to the cosmological constant, generalizes Unimodular Gravity, and proposes an interpretation using Vilenkin's probability flux.

Findings

A new mechanism for the cosmological constant problem is proposed.

The four-form field is related to the Chern-Simons density and time.

A method avoiding Euclidean action using probability flux is developed.

Abstract

We revisit a mechanism proposed by Hawking to resolve the cosmological constant problem (and the controversy it generated) to identify possibly more palatable alternatives and explore new connections and interpretations. In particular, through the introduction of a new action coupling the four-form field strength $F = dA$ to the cosmological constant via a dynamical field $\lambda (x)$, a novel Baum-Hawking-Coleman type mechanism is presented. This mechanism can be seen as a generalisation of Unimodular Gravity. A theory with a similar coupling to "$F^2$" is also presented, with promising results. We show how in such theories the 3-form is closely related to the Chern-Simons density, and its associated definition of time. On the interpretational front, we propose a method avoiding the standard Euclidean action prescription, which makes use of Vilenkin's probability flux.