Recent developments on matter dynamics within the Kaluza-Klein picture

In this paper we propose a new approach to matter dynamics in compactified Kaluza-Klein theories. We discard the idea that the motion is geodesic and perform a simultaneous reduction of matter geometry defining the test particle via a multipole approach. In the resulting dynamics the tower of huge massive modes is removed, without giving up the compactification scenario. Such an approach yields a consistent modified gravity theory with source. Some scenarios and applications to dark energy problem are sketched.