Stability of Flat Space to Singular Instantons

TL;DR

This paper demonstrates that, contrary to previous claims, infinite flat space remains stable against decay through singular instantons when these are properly defined within the path integral framework.

Contribution

It clarifies the stability of flat space by showing that singular instantons do not have negative modes when correctly constrained, resolving prior debates.

Findings

Singular instantons can be well-defined with proper constraints.

Flat space is stable against decay via these instantons.

Previous claims of instability are addressed and refuted.

Abstract

Hawking and the author have proposed a class of singular, finite action instantons for defining the initial conditions for inflation. Vilenkin has argued they are unacceptable. He exhibited an analogous class of asymptotically flat instantons which on the face of it lead to an instability of Minkowski space. However, all these instantons must be defined by introducing a constraint into the path integral, which is then integrated over. I show that with a careful definition these instantons do not possess a negative mode. Infinite flat space is therefore stable against decay via singular instantons.