Using the recent observations of the relation between the Hartle-Hawking wave function and the topological string partition function, we propose a wave function for scalar metric fluctuations on ${\mathbf{S}}^3$ embedded in a Calabi-Yau manifold. This problem maps to a study of noncritical bosonic string propagating on a circle at the self-dual radius. This can be viewed as a stringy toy model for a quantum cosmology.

• Received 20 January 2006

DOI:https://doi.org/10.1103/PhysRevD.73.066009