Singular cosmological instantons made regular

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 1. We show that if the underlying regular manifold is taken to have the topology of RP⁴ 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 RP³ submanifold. For instantons with two singularities, the corresponding topology is that of a cylinder S³×[0,1] with D=4 analogues of “cross-caps” at each of the end points.