paper

Operator ordering and consistency of the wavefunction of the Universe

arXiv:gr-qc/9807075 · doi:10.1103/PhysRevD.59.063513

Abstract

We demonstrate in the context of the minisuperspace model consisting of a closed Friedmann-Robertson-Walker universe coupled to a scalar field that Vilenkin's tunneling wavefunction can only be consistently defined for particular choices of operator ordering in the Wheeler-DeWitt equation. The requirement of regularity of the wavefunction has the particular consequence that the probability amplitude, which has been used previously in the literature in discussions of issues such as the prediction of inflation, is likewise ill-defined for certain choices of operator ordering with Vilenkin's boundary condition. By contrast, the Hartle-Hawking no-boundary wavefunction can be consistently defined within these models, independently of operator ordering. The significance of this result is discussed within the context of the debate about the predictions of semiclassical quantum cosmology. In particular, it is argued that inflation cannot be confidently regarded as a "prediction" of the tunneling wavefunction, for reasons similar to those previously invoked in the case of the no-boundary wavefunction. A synthesis of the no-boundary and tunneling approaches is argued for.

9 pages, epsf, revTeX-3.1, 1 figure. In revised version (v2) a new section etc with additional arguments increases the length of paper by 3 pages of Physical Review; several references added. v3: small typos fixed

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