Szekeres Universes with GUP corrections

TL;DR

This work analyzes how a minimum-length Generalized Uncertainty Principle (GUP) modifies the classical, inhomogeneous Szekeres cosmologies by deforming the underlying Hamiltonian structure. Using a quadratic GUP, the authors derive a modified Szekeres system with perturbative terms proportional to $\beta f(p)$ and recast it as a dimensionless dynamical system in variables $\Omega_{m}$, $\Sigma$, $A$, and $\Omega_{R}$, revealing new asymptotic behavior. The results show that GUP corrections can induce cosmic acceleration and alter spatial curvature, including the emergence of acceleration attractors and a new stationary point $P_{7}$ for $\beta\neq0$, with further changes when a cosmological constant is included. This work highlights how quantum-gravity-inspired minimal-length effects can influence large-scale, inhomogeneous cosmologies and suggests extensions to explicit deformed algebras and the Extended Uncertainty Principle.

Abstract

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.