Wave Function of the Universe
Jul, 1983
46 pages
Published in:
- Phys.Rev.D 28 (1983) 2960-2975,
- Adv.Ser.Astrophys.Cosmol. 3 (1987) 174-189
Report number:
- PRINT-83-0937 (CAMBRIDGE)
Citations per year
Abstract: (APS)
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 Λ>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.- astrophysics: wave function
- boundary condition
- vacuum state
- field theory: de Sitter
- path integral
- supersymmetry
- quantum gravity: Euclidean
- approximation: semiclassical
- Wheeler-DeWitt equation
- topology
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