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Quantum cosmology with scalar fields: Self-adjointness and cosmological scenarios

Abstract

We discuss the issue of unitarity in particular quantum cosmological models with scalar fields. The time variable is recovered, in this context, by using the Schutz formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases in which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even in the cases not exhibiting a unitary evolution, a formal computation of the expectation value of the scale factor indicates a nonsingular bounce. The importance of unitary evolution in quantum cosmology is briefly discussed.

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Correspondence to Carla R. Almeida.

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Almeida, C.R., Batista, A.B., Fabris, J.C. et al. Quantum cosmology with scalar fields: Self-adjointness and cosmological scenarios. Gravit. Cosmol. 21, 191–199 (2015). https://doi.org/10.1134/S0202289315030020

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Keywords

  • Wave Packet
  • Hamiltonian Operator
  • Unitary Evolution
  • Quantum Cosmology
  • Cosmological Scenario