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

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

Sep 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988nuphb.306..931p&link_type=abstract

Nuclear Physics B, Volume 306, Issue 4, p. 931-945.

Physics

Nuclear Physics

11

Scientific paper

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 L = -1/24βR2, 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 L = (1/2ɛφ2R-1/4λ φ4) can be similarly analyzed. Inclusion of a kinetic term 1/2φkφk destroys this similarly, which is restored however upon addition of a term (-1/24βR2).
Address from 22nd October, 1987.

Affiliated with

Also associated with

No associations

Rating

On the semi-classical approximation to the wave function of the universe and its stochastic interpretation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the semi-classical approximation to the wave function of the universe and its stochastic interpretation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the semi-classical approximation to the wave function of the universe and its stochastic interpretation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-915171