Abstract
We argue that the indefiniteness of the Euclidean Einstein action is more serious in the cosmological context than in the asymptotically Euclidean context. To correct this, we consider a positive-definite action containing quadratic curvature terms. The physical states Ψ are now functions of both a three-metric and extrinsic curvature , and satisfy a differential equation analogous to the Wheeler-DeWitt equation. This equation has the form of a Schrödinger equation with playing the role of ‘‘time.’’ By adopting Hartle and Hawking’s boundary condition on the Euclidean function integral, we obtain a ‘‘preferred’’ solution to this equation. It is shown that in a simple minisuperspace model this wave function describes an inflationary universe.
- Received 9 October 1984
DOI:https://doi.org/10.1103/PhysRevD.31.1169
©1985 American Physical Society