Abstract
The classical cosmology of flat space can be realized in a phenomenological scalar field model for dark energy : a two-field model of quintessence and phantom fields. When the model is supplied by a proper field mixing term it becomes analytically solvable for exponential potentials. The motivation is given for replacing a phantom field by a normal pseudoscalar field with complex but PT-symmetric potential (PTom). The comparison of two approaches in their prediction for the fate of our Universe is done in figures. The quantum cosmology of flat space is realized in the Arnowitt-Deser-Misner approach by means of the Wheeler-DeWitt equations . Taking into account the isotropy and homogeneity of space the ADM approach is reduced to only quantized component of space-time metric—Friedmann-Robertson-Walker factor. The quantum models supplied with appropriate mixing kinetic terms turn out to be also integrable for exponential potentials and the exact analytical solutions are obtained for wave functionals of quantum PT symmetric cosmology . Lessons and perspectives for developing PT symmetric Classical and Quantum Cosmology are discussed.
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Acknowledgments
The work is done with financial support by grants RFBR 13-02-00127 and 16-02-00348 as well as by the Saint Petersburg State University grant 11.41.775.2015. A.A. is grateful to the organizers of the 15th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, Palermo for the hospitality.
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Andrianov, A.A., Lan, C., Novikov, O.O. (2016). PT Symmetric Classical and Quantum Cosmology. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_3
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