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Title: Wave function of the Universe

Abstract

The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the ''ground state'' or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and ..lambda..>0. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier tomore » a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.« less

Authors:
;
Publication Date:
Research Org.:
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 and Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
OSTI Identifier:
5310722
Resource Type:
Journal Article
Journal Name:
Phys. Rev. D; (United States)
Additional Journal Information:
Journal Volume: 28:12
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; UNIVERSE; WAVE FUNCTIONS; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FEYNMAN PATH INTEGRAL; HAMILTONIANS; PROBABILITY; PROPAGATOR; QUANTUM MECHANICS; SCALAR FIELDS; EQUATIONS; FUNCTIONS; INTEGRALS; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS; 640106* - Astrophysics & Cosmology- Cosmology; 645400 - High Energy Physics- Field Theory

Citation Formats

Hartle, J.B., and Hawking, S.W.. Wave function of the Universe. United States: N. p., 1983. Web. doi:10.1103/PhysRevD.28.2960.
Hartle, J.B., & Hawking, S.W.. Wave function of the Universe. United States. doi:10.1103/PhysRevD.28.2960.
Hartle, J.B., and Hawking, S.W.. Thu . "Wave function of the Universe". United States. doi:10.1103/PhysRevD.28.2960.
@article{osti_5310722,
title = {Wave function of the Universe},
author = {Hartle, J.B. and Hawking, S.W.},
abstractNote = {The quantum state of a spatially closed universe can be described by a wave function which is a functional on the geometries of compact three-manifolds and on the values of the matter fields on these manifolds. The wave function obeys the Wheeler-DeWitt second-order functional differential equation. We put forward a proposal for the wave function of the ''ground state'' or state of minimum excitation: the ground-state amplitude for a three-geometry is given by a path integral over all compact positive-definite four-geometries which have the three-geometry as a boundary. The requirement that the Hamiltonian be Hermitian then defines the boundary conditions for the Wheeler-DeWitt equation and the spectrum of possible excited states. To illustrate the above, we calculate the ground and excited states in a simple minisuperspace model in which the scale factor is the only gravitational degree of freedom, a conformally invariant scalar field is the only matter degree of freedom and ..lambda..>0. The ground state corresponds to de Sitter space in the classical limit. There are excited states which represent universes which expand from zero volume, reach a maximum size, and then recollapse but which have a finite (though very small) probability of tunneling through a potential barrier to a de Sitter-type state of continual expansion. The path-integral approach allows us to handle situations in which the topology of the three-manifold changes. We estimate the probability that the ground state in our minisuperspace model contains more than one connected component of the spacelike surface.},
doi = {10.1103/PhysRevD.28.2960},
journal = {Phys. Rev. D; (United States)},
number = ,
volume = 28:12,
place = {United States},
year = {1983},
month = {12}
}