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Quantum potentiality in Inhomogeneous Cosmology

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.