1998/07/31 by N. Kontoleon, Nectarios Kontoleon, David L. Wiltshire +1 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.59.063513
published as Phys.Rev. D59 (1999) 063513 · 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
openalex publication_date 1999/02/24 · arxiv created 1999/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 wave function can only be consistently defined for particular choices of operator ordering in the Wheeler-DeWitt equation. The requirement of regularity of the wave function 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 wave function 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 wave function, for reasons similar to those previously invoked in the case of the no-boundary wave function. A synthesis of the no-boundary and tunneling approaches is argued for.