Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

202 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
Assuming the solutions are
where is the confluent hypergeometricfunction, and are
arbitrary separation constants and
3.3. EXACT SOLUTIONS FOR BIANCHI II
WITH
In this case the potential for is given as follows
and the WDW equation is given by
the wavefunction takes the final form
where and
and the are integration constants.
4. FINAL REMARKS
We have obtained exact solutions for quantum and classical cosmologies
in the general scalar–tensor theory of gravitation with arbitrary coupling
function and particular potentials We have constructed
quantum wormholes solutions. The Bianchi I,II solutions are for arbitrary
large anisotropies. Quantum cosmology using general relativity
in homogeneous spacetimes with small anisotropies and a scalar field
were considered by Lukash and Schmidt and Amsterdamski [12]. Lidsey