On the semi-classical approximation to the wave function of the universe and its stochastic interpretation

Pollock, M.D.

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/3201

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DC Field	Value	Language
dc.contributor.author	Pollock, M.D.	-
dc.date.accessioned	2007-06-30T10:48:17Z	-
dc.date.available	2007-06-30T10:48:17Z	-
dc.date.issued	1988-09	-
dc.identifier.citation	Nuclear Physics B, 1988, Vol.306, p931-945	en
dc.identifier.issn	0550-3213	-
dc.identifier.uri	http://hdl.handle.net/2289/3201	-
dc.description	Restricted Access.	en
dc.description.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.	en
dc.format.extent	603822 bytes	-
dc.format.mimetype	application/pdf	-
dc.language.iso	en	en
dc.publisher	Elsevier B.V.	en
dc.relation.uri	http://dx.doi.org/10.1016/0550-3213(88)90448-8	en
dc.rights	1988 Elsevier B.V.	en
dc.title	On the semi-classical approximation to the wave function of the universe and its stochastic interpretation	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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