Abstract
We use the Brans-Dicke theory from the framework of General Relativity (Einstein frame), but now the total energy momentum tensor fulfills the following condition \([\frac{1}{\phi}T^{\mu \nu M}+T^{\mu \nu}(\phi)]_{;\nu}=0\). We take as a first model the flat FRW metric and with the law of variation for Hubble’s parameter proposal by Berman and Gomide (Nuovo Cimento B 74: 182, 1983), we find solutions to the Einstein field equations by the cases: inflation (γ=−1), radiation (\(\gamma=\frac{1}{3}\)), stiff matter (γ=1). For the Inflation case the scalar field grows fast and depends strongly of the constant M γ=−1 that appears in the solution, for the Radiation case, the scalar stop its expansion and then decrease perhaps due to the presence of the first particles. In the Stiff Matter case, the scalar field is decreasing so for a large time, ϕ→0. In the same line of classical solutions, we find an exact solution to the Einstein field equations for the stiff matter (γ=1) and flat universe, using the Hamilton-Jacobi scheme.
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Acknowledgements
This work was supported in part by DAIP (2011–2012), Promep UGTO-CA-3 and CONACyT 167335 and 179881 grants. JMR was supported by Promep grant ITESJOCO-001. Many calculations where done by Symbolic Program REDUCE 3.8. This work is part of the collaboration within the Advanced Institute of Cosmology and Red PROMEP: Gravitation and Mathematical Physics under project Quantum aspects of gravity in cosmological models, phenomenology and geometry of space-time.
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Ramírez, J.M., Socorro, J. FRW in Cosmological Self-creation Theory. Int J Theor Phys 52, 2867–2878 (2013). https://doi.org/10.1007/s10773-013-1580-9
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DOI: https://doi.org/10.1007/s10773-013-1580-9