Quantum cosmology with scalar fields: Self-adjointness and cosmological scenarios
- 55 Downloads
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.
KeywordsWave Packet Hamiltonian Operator Unitary Evolution Quantum Cosmology Cosmological Scenario
Unable to display preview. Download preview PDF.
- 4.N. Pinto-Neto, “Quantum cosmology,” in Cosmology and Gravitation, Ed. M. Novello (Editions Frontieres, Gif-sur-Yvette, 1996).Google Scholar
- 5.K. Kuchar, “Time and interpretation of quantum gravity,” in Proc. 4th Canadian Conference on General Relativity and Relativistic Astrophyscis (World Scientific, Singapore, 1992).Google Scholar
- 12.P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1983).Google Scholar
- 23.I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, San Diego, 2007).Google Scholar
- 24.M. Reed and B. Simon, Methods of ModernMathematical Physics (Academic Press, New York, 1975), Vol. 2.Google Scholar