Quantization of inhomogeneous spacetimes with cosmological constant term

Abstract

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.

arXiv comment11 pages, 2 figures

References in corpus (23)

• Beginning inflation in an inhomogeneous universe
• Can Bohmian mechanics be made relativistic?
• Robustness of Inflation to Inhomogeneous Initial Conditions
• Lie - point and variational symmetries in minisuperspace Einstein's gravity
• Szekeres Swiss-Cheese model and supernova observations
• Integrability of irrotational silent cosmological models
• Dynamics of Silent Universes
• The Szekeres Swiss Cheese model and the CMB observations
• A novel approach to the dynamics of Szekeres dust models
• The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations
• The growth of structure in the Szekeres inhomogeneous cosmological models and the matter-dominated era
• Consistency of dust solutions with div H=0
• Symmetries and Singularities of the Szekeres System
• Szekeres Universes with Homogeneous Scalar Fields
• Partially locally rotationally symmetric perfect fluid cosmologies
• Symmetry and Equivalence in Szekeres Models
• Variational Contact Symmetries of Constraint Lagrangians
• Quantization of the Szekeres System
• Szekeres models: a covariant approach
• Cyclic Szekeres Universes
• Inhomogeneous spacetimes in Einstein-æther Cosmology
• Inhomogeneous spacetimes in Weyl integrable geometry with matter source
• Intrinsic Conformal Symmetries in Szekeres models

Cited by in corpus (5)

• Eisenhart--Duval lift for minisuperspace quantum cosmology
• Phase space analysis of the bouncing universe with stringy effects
• Quantum potentiality in Inhomogeneous Cosmology
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe