Open Inflation, the Four Form and the Cosmological Constant

TL;DR

This paper integrates a four-form field from supergravity into open inflation to tackle the cosmological-constant problem via anthropic selection. By formulating the Euclidean action in the momentum representation and carefully accounting for boundary terms and a singular south pole, the authors derive a calculable prior for Λ and show that the galaxy-formation likelihood largely governs the observed small Λ, while allowing for a nonzero Λ and an open universe. The approach yields a near-flat prior for Λ over anthropically allowed ranges and predicts a universe that is open with a small but nonzero Λ, though it acknowledges unresolved issues regarding the present value of Ω_0 and the role of potentials with local maxima. Overall, the work provides a first-principles framework linking four-form dynamics, singular instantons, and anthropic reasoning to cosmological parameter inference in open inflation.

Abstract

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation (hep-th/9802030) allows an anthropic solution to the cosmological constant problem in which the cosmological constant gives a small but non-negligible contribution to the density of today's universe. We include a discussion of the role of the singularity in our solution and a reply to Vilenkin's recent criticism (hep-th/9803084).