literature

Wave Function of the Universe

Jul, 1983
46 pages
Part of QUANTUM COSMOLOGY, 174-189
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

19811992200320142025020406080100120
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