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The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity.\udThe 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.\ud\udThe second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-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

The relation between geometry and matter in classical and quantum gravity and cosmology