Wave function of the Universe

@article{citeulike:1875857, 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 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.}, author = {Hartle, J. B. and Hawking, S. W. }, citeulike-article-id = {1875857}, doi = {http://dx.doi.org/10.1103/PhysRevD.28.2960}, journal = {Physical Review D}, keywords = {cosmology}, month = {December}, number = {12}, pages = {2960+}, posted-at = {2007-11-07 01:28:54}, priority = {2}, publisher = {American Physical Society}, title = {Wave function of the Universe}, url = {http://dx.doi.org/10.1103/PhysRevD.28.2960}, volume = {28}, year = {1983} }

TY - JOUR ID - citeulike:1875857 L3 - citeulike-article-id:1875857 N2 - 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. IS - 12 JF - Physical Review D TI - Wave function of the Universe PB - American Physical Society VL - 28 SP - 2960 KW - cosmology AU - Hartle, JB AU - Hawking, SW PY - 1983/12/15/ UR - http://dx.doi.org/10.1103/PhysRevD.28.2960 ER -