Wave function of the Universe

Journal Article · Thu Dec 15 04:00:00 EST 1983 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.28.2960· OSTI ID:5310722

Hartle, J B; Hawking, S W

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.

• Research Organization: Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637 and Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
• OSTI ID: 5310722
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 28:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
645400 -- High Energy Physics-- Field Theory
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FEYNMAN PATH INTEGRAL
FUNCTIONS
HAMILTONIANS
INTEGRALS
MATHEMATICAL OPERATORS
MECHANICS
PROBABILITY
PROPAGATOR
QUANTUM MECHANICS
QUANTUM OPERATORS
SCALAR FIELDS
UNIVERSE
WAVE FUNCTIONS