  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 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.
