The dynamics of extended bodies endowed with multipolar structure up to the mass quadrupole moment is investigated in the Schwarzschild background according to Dixon's model, extending previous works. The whole set of evolution equations is numerically integrated under the simplifying assumptions of constant frame components of the quadrupole tensor and that the motion of the center of mass be confined on the equatorial plane, the spin vector being orthogonal to it.

The gravitational field of a static body with the quadrupole moment is described by an exact solution found by Erez and Rosen. Here, we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables such as image positions and magnification have been explicitly obtained in the weak-field and small quadrupole limit. In this limit, the spacetime metric appears as the natural generalization to quadrupole corrections of the metric form adopted also in current astrometric models.

The optical medium analogy of a radiation field generated by either an exact gravitational plane wave or an exact electromagnetic wave in the framework of general relativity is developed. The equivalent medium of the associated background field is inhomogeneous and anisotropic in the former case, whereas it is inhomogeneous but isotropic in the latter. The features of light scattering are investigated by assuming the interaction region to be sandwiched between two flat spacetime regions, where light rays propagate along straight lines.

We evaluate the modifications to the cosmic microwave background anisotropy spectrum that result from a semiclassical expansion of the Wheeler-DeWitt equation. Recently, such an investigation in the case of a real scalar field coupled to gravity has led to the prediction that the power at large scales is suppressed. We make here a more general analysis and show that there is an ambiguity in the choice of solution to the equations describing the quantum gravitational effects. Whereas one of the two solutions describes a suppression of power, the other one describes an enhancement.

We complete the analytical determination, at the 4th post-Newtonian approximation, of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies. The (non logarithmic) coefficient $a_5(\nu)$ measuring this 4th post-Newtonian interaction potential is found to be linear in the symmetric mass ratio $\nu$. Its $\nu$-independent part $a_5(0)$ is obtained by an analytical gravitational self-force calculation that unambiguously resolves the formal infrared divergencies which currently impede its direct post-Newtonian calculation.