RRI Digital Repository >
07. Theoretical Physics >
Research Papers (TP) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/2289/3201

Title:  On the semiclassical approximation to the wave function of the universe and its stochastic interpretation 
Authors:  Pollock, M.D. 
Issue Date:  Sep1988 
Publisher:  Elsevier B.V. 
Citation:  Nuclear Physics B, 1988, Vol.306, p931945 
Abstract:  In quantum cosmology, a wave function ψ for a given theory can be obtained by solving the WheelerDeWitt equation, using the semiclassical 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 quaside Sitter spacetime, then it is possible to derive a FokkerPlanck equation for the probability distribution P, as shown by Starobinsky. Arguing by analogy with quantum mechanics in flat spacetime, one would expect that P ∝ ψψ*. We examine this assertion by reference to the scaleinvariant theory Image, whose wave function has been calculated in minisuperspace by Horowitz, and those classical solutions are de Sitter spacetimes. It appears that deviations from the relation P ∝ ψψ* are attributable to longwavelength fluctuations δφe ≈ H/2π in the effective inflation field φe = √βR = √12β H. Their existence is taken into account in the derivation of the FokkerPlanck equation, but not in the derivation of ψ when this is restricted to minisuperspace. 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:  05503213 
Alternative Location:  http://dx.doi.org/10.1016/05503213(88)904488 
Copyright:  1988 Elsevier B.V. 
Appears in Collections:  Research Papers (TP)

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
