Dynamics of a Classical Bi-Metric Cosmology with GUP-Deformed Poisson Brackets

This work analyzes a bi-metric cosmological model where two sectors, characterized by their respective scale factors, interact through a deformed Poisson bracket structure. This deformation is based on the Generalized Uncertainty Principle (GUP). Through a numerical analysis, we study how this interaction affects the expansion dynamics. The results indicate that for positive values of the deformation parameter, the coupling induces an acceleration that leads to a Big Rip singularity in finite time, even in the absence of a cosmological constant. A power-law relation is established between the deformation parameter and the critical time of divergence for the scale factors. Finally, the regime with a negative deformation parameter is also investigated. In this case, the symplectic structure becomes singular, leading to the contraction of one sector and the freezing of the other.