Singular Instantons Made Regular

TL;DR

This paper presents a method to regularize singular cosmological instantons by using a conformal transformation with a twisted field, leading to a family of solutions with minimal action configurations on noncontractible manifolds.

Contribution

It introduces a novel regularization technique for Hawking-Turok instantons via conformal transformations with twisted fields, revealing new solution families on nontrivial topologies.

Findings

Regularization of singular instantons through conformal transformation.

Existence of a one-parameter family of solutions with minimal action.

Solutions characterized by noncontractible $RP^4$ and $RP^3$ submanifolds.

Abstract

The singularity present in cosmological instantons of the Hawking-Turok type is resolved by a conformal transformation, where the conformal factor has a linear zero of codimension one. We show that if the underlying regular manifold is taken to have the topology of $RP^4$, and the conformal factor is taken to be a twisted field so that the zero is enforced, then one obtains a one-parameter family of solutions of the classical field equations, where the minimal action solution has the conformal zero located on a minimal volume noncontractible $RP^3$ submanifold. For instantons with two singularities, the corresponding topology is that of a cylinder $S^3\times [0,1]$ with D=4 analogues of `cross-caps' at each of the endpoints.