J. Socorro, Juan M. Ramírez
We use the Brans-Dicke theory in the Einstein frame but with the total energy momentum tensor $\rm [\frac{1}{\phi}T^{\mu \nu M}+T^{\mu \nu}(\phi)]_{;\nu}=0$. We take as a first model the flat FRW metric and with the law of variation for Hubble's parameter proposal by Berman \cite{Berman}, we find solutions to the Einstein field equations by two cases: stiff matter ($\gamma=1$), inflation ($\gamma=-1$). For the inflation case the scalar field depends strongly of the constant $\rm M_{\gamma=-1}$ that appears in the solution, an in the stiff matter case we found an oscillatory solution for the scalar field. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter and flat universe, using the Hamilton-Jacobi scheme. Also, we solve the corresponding quantum Wheeler-DeWitt equation for this model, and found the structure of wavefunction.
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http://arxiv.org/abs/1206.5413
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