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Title: | On the semi-classical approximation to the wave function of the universe and its stochastic interpretation |
Authors: | Pollock, M.D. |
Issue Date: | Sep-1988 |
Publisher: | Elsevier B.V. |
Citation: | Nuclear Physics B, 1988, Vol.306, p931-945 |
Abstract: | In quantum cosmology, a wave function ψ for a given theory can be obtained by solving the Wheeler-DeWitt equation, using the semi-classical approximation to the path integral over euclidean metrics to impose the boundary condition, as described by Hawking and his collaborators. If the universe is expanding as a quasi-de Sitter space-time, then it is possible to derive a Fokker-Planck equation for the probability distribution P, as shown by Starobinsky. Arguing by analogy with quantum mechanics in flat space-time, one would expect that P ∝ ψψ*. We examine this assertion by reference to the scale-invariant theory Image, whose wave function has been calculated in mini-superspace by Horowitz, and those classical solutions are de Sitter space-times. It appears that deviations from the relation P ∝ ψψ* are attributable to long-wavelength fluctuations δφe ≈ H/2π in the effective inflation field φe = √βR = √12β H. Their existence is taken into account in the derivation of the Fokker-Planck equation, but not in the derivation of ψ when this is restricted to mini-superspace. In the limit β → ∞, we find that δφe/φe → 0 and that P ∝ ψψ*. The scale invariant theory Image) can be similarly analyzed. Inclusion of a kinetic term Image destroys this similarly, which is restored however upon addition of a term Image. |
Description: | Restricted Access. |
URI: | http://hdl.handle.net/2289/3201 |
ISSN: | 0550-3213 |
Alternative Location: | http://dx.doi.org/10.1016/0550-3213(88)90448-8 |
Copyright: | 1988 Elsevier B.V. |
Appears in Collections: | Research Papers (TP) |
Files in This Item:
File | Description | Size | Format | |
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1988 NP-B V306 p931.pdf Restricted Access | Restricted Access | 589.67 kB | Adobe PDF | View/Open Request a copy |
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