Physics
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1426p&link_type=abstract
"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R
Physics
Scientific paper
The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for the Bianchi types I and II cosmologies. The coupling function ω(ɸ) is kept arbitrary and the selfinteracting potential is chosen to obtain exact solutions. For Bianchi I, exact solutions are found for two selfinteracting potentials, one linear in the scalar field and another more complicated, whose precise form depend on the coupling function ω(ɸ), in the case of Brans-Dicke theory it is polynomial in the scalar field in the Jordan frame, and it is a combiantion of exponentials in the Einstein frame. A family of solutions satisfying the Hawking-Page regularity conditions for wormholes is found. That is that the wavefunctions satisfy the following conditions: i) The wavefunctions vanish at spatial infinity and ii) the wavefunctioins do not oscillate when the spatial volume vanishes. The WKB wavefunctions for both potentials are obtained. For the Bianchi type II exact solutions are found only for vanishing potential and the WKB wavefunctions are obtained. An interesting point about these toys models is that the classical solutions are already known or obtained in this work and therefore the quantum to classical transition can be studied with them.
Mora Cesar
Pimentel Luis O.
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