Quantum cosmology with a positive-definite action

Details Quantum cosmology with a positive-definite action Quantum cosmology with a positive-definite action

Mar 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phrvd..31.1169h&link_type=abstract

Physical Review D (Particles and Fields), Volume 31, Issue 6, 15 March 1985, pp.1169-1177

Mathematics

Logic

62

Scientific paper

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 qab and extrinsic curvature Kab, and satisfy a differential equation analogous to the Wheeler-DeWitt equation. This equation has the form of a Schrödinger equation with qab 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.

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