Quantum fluctuations of the compact phase space cosmology. (English) Zbl 1481.83093
Summary: In the recent article [the aithors, Phys. Rev. D 100, No. 4, Article ID 043533, 15 p, (2019; doi:10.1103/PhysRevD.100.043533)] a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and the quantum theory is characterized by finite dimensional Hilbert space. Furthermore, by considering the \(\mathbb{S}^2\) phase space, quantum description is constructed with the use SU(2) representation theory. The purpose of this article is to apply effective methods to analyze quantum dynamics of the model at the semi-classical regime. The analysis is performed both without prior solving of the quantum constraint and by extracting physical Hamiltonian of the model. At the effective level, the results of the two procedures are shown to be equivalent. We find a nontrivial behavior of the fluctuations around the recollapse of the Universe, which is distinct from what is found after quantization with the standard flat phase space. The behavior is reflected at the level of the modified Friedmann equation with quantum back-reaction effects, which is derived. Finally, a relation between quantum fluctuations in the minisuperspace model under consideration and the Bousso bound has been found. It has been shown that the Bousso bound can be violated for certain choices of semiclassical states.
MSC:
| 83F05 | Relativistic cosmology |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 83C45 | Quantization of the gravitational field |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
| 81T33 | Dimensional compactification in quantum field theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81T12 | Effective quantum field theories |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
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