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Quantization of inhomogeneous spacetimes with cosmological constant term. (English) Zbl 1482.83063

Summary: We show that the Szekeres system with cosmological constant admits a sufficient number of conservation laws, which allow to claim the integrability of the system. The main novelty in this investigation is that we find that the unique attractor of the Szekeres system is the isotropic inhomogeneous de Sitter (-like) Universe, contrary to the original system in which the attractors describe Kantowski-Sachs (-like) spacetimes. We also study the existence of quantum corrections and the emergence of classicality by considering the linear and quadratic conserved quantities at the quantum level. We perform an analysis considering different approaches, involving the Bohmian quantum potential and a probability analysis. The result is that there are no quantum corrections for the quadratic integrals, while there exists a linear case for which we find quantum corrections.

MSC:

83C45 Quantization of the gravitational field
83F05 Relativistic cosmology
17B81 Applications of Lie (super)algebras to physics, etc.
11K60 Diophantine approximation in probabilistic number theory
83C40 Gravitational energy and conservation laws; groups of motions
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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