Quantum potentiality in Inhomogeneous Cosmology

TL;DR

This paper explores the quantum potential in inhomogeneous Szekeres cosmological models using canonical quantization, revealing quantum corrections that alter classical properties and introduce new asymptotic solutions.

Contribution

It introduces a novel quantum analysis of the Szekeres system, identifying conservation laws and deriving quantum corrections that modify classical inhomogeneous cosmological solutions.

Findings

Quantum potential modifies the Szekeres system dynamics.

Quantum corrections violate the silent property of Szekeres spacetimes.

New asymptotic solutions with anisotropic fluid emerge due to quantum effects.

Abstract

For the Szekeres system which describes inhomogeneous and anisotropic spacetimes we make use of a point-like Lagrangian, which describes the evolution of the physical variables of the Szekeres model, in order to perform a canonical quantization and to study the quantum potentiality of the Szekeres system in the content of de Broglie--Bohm theory. We revise previous results on the subject and we find that for a specific family of trajectories with initial conditions which satisfy a constraint equation, there exists additional conservation laws for the classical Szekeres system which are used to define differential operators and to solve the Wheeler-DeWitt equation. From the new conservation laws we construct a wave function which provides a nonzero quantum potential term that modifies the Szekeres system. The quantum potential corresponds to new terms in the dynamical system such that new asymptotic solutions with a nonzero energy momentum tensor of an anisotropic fluid exist. Therefore, the silent property of the Szekeres spacetimes is violated by quantum correction terms.