Positive curvature and scalar field tunneling in the landscape

TL;DR

This paper models vacuum tunneling involving a scalar field in a positively curved space, showing that such tunneling can produce an inflating universe with residual positive curvature, which may be detectable.

Contribution

It introduces a new model of scalar field vacuum tunneling that results in an inflating universe with positive curvature, expanding understanding of landscape tunneling scenarios.

Findings

Existence of a parametric regime where the solution is self-consistent.

Tunneling can produce an inflating universe with residual positive curvature.

Positive curvature detection does not exclude a tunneling origin.

Abstract

We present a model of vacuum tunneling through a classically forbidden region where a scalar field changes its value simultaneously over the entire volume of a (meta)stable ancestor vacuum with spherical curvature. The tunneling leaves the geometry unchanged but rearranges the energetic contributions of the matter sources, leading to an inflating solution with residual positive curvature. We show that there exists a parametric regime where this solution is self-consistent and dominates the overall tunneling rate. We conclude that an experimental detection of positive curvature, while not necessarily likely, therefore does not rule out the possibility that our present observer patch originated from semiclassical vacuum tunneling in a string or field theoretic landscape.