Quantization of inhomogeneous spacetimes with cosmological constant term

TL;DR

This paper demonstrates the integrability of the Szekeres system with a cosmological constant, identifies its attractor as an isotropic de Sitter universe, and explores quantum corrections, finding none for quadratic integrals but some for linear ones.

Contribution

It introduces the integrability of the Szekeres system with a cosmological constant and analyzes quantum corrections using various approaches.

Findings

The Szekeres system with cosmological constant is integrable due to conservation laws.

The attractor of the system is an isotropic inhomogeneous de Sitter universe.

No quantum corrections are found for quadratic conserved quantities, but some linear corrections exist.

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.