Open inflation and the singular boundary - art. no. 047301

The singularity in the Hawking-Turok model of open inflation has some appea ling properties, such as the fact that its action is integrable. Also, if o ne thinks of the singularity as the boundary of spacetime, then the Gibbons -Hawking term is nonvanishing and finite. Here, we consider a model where t he gravitational and scalar fields are coupled to a dynamical membrane. The singular instanton can then be obtained as the limit of a family of "no-bo undary" solutions where both the geometry and the scaler field are regular, Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking term. Unrelated to this issue, w e also point out that the singularity acts as a reflecting boundary for sca lar perturbations and gravity waves. Therefore, the quantization of cosmolo gical perturbations seems to be well posed in this background.