Open inflation and the singular boundary

TL;DR

This paper proposes a regularization method for the singularity in open inflation models, showing that the singularity's contribution to the Euclidean action is limited and that scalar perturbations are better behaved near the boundary.

Contribution

It introduces a matter-based regularization of the singularity in open inflation, connecting singular instantons to regular no-boundary solutions and analyzing perturbation behavior.

Findings

Singularity contribution to Euclidean action is 1/3 of Gibbons-Hawking term

Gravitational backreaction improves scalar perturbation behavior

Quantization of perturbations becomes well-posed near the boundary

Abstract

The singularity in Hawking and Turok's model (hep-th/9802030) of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of ``no-boundary'' solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking boundary term. Unrelated to this question, we also point out that gravitational backreaction improves the behaviour of scalar perturbations near the singularity. As a result, the problem of quantizing scalar perturbations and gravity waves seems to be very well posed.