Problem of the boundary condition in quantum cosmology - A simple example

Details Problem of the boundary condition in quantum cosmology - A simple example Problem of the boundary condition in quantum cosmology - A simple example

Oct 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5.1357z&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, Oct. 1, 1988, p. 1357-1365.

Mathematics

Logic

4

Boundary Conditions, Boundary Value Problems, Cosmology, Quantum Theory, Space-Time Functions, Big Bang Cosmology, Conformal Mapping, Gravitation Theory, Perturbation Theory, Potential Theory

Scientific paper

The quantum cosmological minisuperspace model with a massless scalar field with a potential Lambda(phi) exp 4 is investigated. The Hartle-Hawking proposal gives the possibility of picking a particular solution of the Wheeler-DeWitt equation in the space of the imaginary conformal factor a and scalar field phi. An analytic expression for this solution is obtained, and an analytic continuation to the space of real a and phi is performed. The boundary conditions on the surface a = 0, phi = + or - infinity, are psi(a = 0, phi = + or - infinity) = 1. It is shown that near this boundary the psi have exponential behavior. In the region where the interaction between gravity and the scalar field plays the main role, the psi have an oscillation behavior, and this leads to the inflation of the universe.

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