Midisuperspacetime foam and the cosmological constant

TL;DR

Addresses the cosmological constant problem by exploring whether spacetime foam can hide a large vacuum energy ($\Lambda$) from observations. The authors formulate a locally spherically symmetric midisuperspace with topology $S^2\times S^1$, quantize via a dust-time approach to yield a Schrödinger-like Wheeler–DeWitt equation, and solve in the WKB limit to obtain a wave function with phase $S[h,f]$ and parameters such as $\tilde{\Lambda}=\Lambda-\kappa^2 E$ and $\beta$ that encode foam structure. They find that configurations with many layers and random signs $\{\sigma_i\}$ concentrate near necks and can trap probability currents, effectively suppressing macroscopic expansion and hiding a large $\Lambda$. The work provides a concrete quantum gravitational mechanism for a small effective cosmological constant, while noting limitations, open questions, and speculative connections to holography and $1/\sqrt{N}$ scaling.

Abstract

Standard quantum field theory arguments predict an enormous cosmological constant. But what would this mean observationally? For a homogeneous universe the answer is clear, but if the universe is inhomogeneous at the Planck scale, the question becomes more subtle: for a large class of initial data, rapidly expanding and contracting regions coexist and give an average expansion near zero. Classically, such data develop singularities, and we need a quantum description of their evolution. I describe results from a spherically symmetric midisuperspace model, in which the wave function can become trapped for long periods in regions in which the average expansion remains small, effectively hiding a large cosmological constant.