Szekeres Universes with GUP corrections

We demonstrate that introducing a deformed algebra with a minimum length modifies the field equations for an inhomogeneous spacetime, resulting in the emergence of acceleration. Specifically, we examine the analytic effects of the Generalized Uncertainty Principle on the classical field equations of the Szekeres system. Our findings show that the deformed algebra leads to a modified Szekeres system capable of describing cosmic acceleration. Moreover, the spatial curvature of the spacetime is influenced by the presence of the minimum length.

💡 Research Summary

This paper investigates the effects of incorporating the Generalized Uncertainty Principle (GUP) from quantum gravity into the classical dynamics of inhomogeneous cosmological models, specifically the Szekeres universes. The primary motivation is to explore how the fundamental concept of a minimum measurable length (on the order of the Planck length) modifies large-scale cosmic evolution.

The authors begin by reviewing the Szekeres metric, an exact inhomogeneous and anisotropic solution to Einstein’s field equations for a pressureless fluid (dust). The dynamics are governed by the Szekeres system: a set of four first-order differential equations for the expansion rate (θ), shear (σ), matter density (ρ), and the electric part of the Weyl tensor (E). A key step is the reformulation of this system into a Hamiltonian framework, which provides the canonical structure necessary for applying the GUP modifications.

The GUP, which generalizes the standard Heisenberg uncertainty principle to ∆X∆P ≥ (ħ/2)