The relation between Geometry and Matter in classical and quantum Gravity and Cosmology

Abstract: The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide asum-over-histories' formulation of gravitational quantum transition amplitudes: the research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.