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Quantum Cosmological Scenarios of Brans-Dicke Gravity in Einstein and Jordan Frames

Abstract

The Hamiltonian of any quantum cosmological model must obey some conditions in order to be self-adjoint or to admit self-adjoint extensions. We consider the self-adjoint character of the Hamiltonian resulting from the Brans-Dicke theory, both in Einstein and Jordan frames. In both cases we find the wave-function solutions in order to obtain concrete predictions for the evolution of the Universe. We show that the specific cosmological scenarios obtained depend very weakly on the conditions of having a self-adjoint operator. The problem of equivalence between the Einstein and Jordan frames is considered, and it is shown that this equivalence implies a specific ordering parameter as well as a particular choice of the physical variables.

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Correspondence to C. R. Almeida.

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Almeida, C.R., Batista, A.B., Fabris, J.C. et al. Quantum Cosmological Scenarios of Brans-Dicke Gravity in Einstein and Jordan Frames. Gravit. Cosmol. 24, 245–253 (2018). https://doi.org/10.1134/S0202289318030027

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