Dark gravitational sectors on a generalized scalar-tensor vector bundle model and cosmological applications

In this work we present the foundations of generalized scalar-tensor theories arising from vector bundle constructions, and we study the kinematic, dynamical, and cosmological consequences. In particular, over a pseudo-Riemannian space-time base manifold, we define a fiber structure with two scalar fields. The resulting space is a 6-dimensional vector bundle endowed with a nonlinear connection. We provide the form of the geodesics and the Raychaudhuri and general field equations, both in the Palatini and metrical methods. When applied at a cosmological framework, this novel geometrical structure induces extra terms in the modified Friedmann equations, leading to the appearance of an effective dark energy sector, as well as of an interaction of the dark mater sector with the metric. We show that we can obtain the standard thermal history of the universe, with the sequence of matter and dark-energy epochs, and furthermore the effective dark-energy equation-of-state parameter can lie in the quintessence or phantom regimes, or exhibit the phantom-divide crossing.