The early universe, the present universe

Almost ten years ago Gasperini and Veneziano proposed a new picture of the very primordial Universe (z much greater than 1) based on string theory, called the pre-big-bang scenario. Here we review the key ideas of this model, its main phenomenological consequences, and the most striking differences with respect to ordinary inflationary models. The second part of this Proceedings is concerned with cosmology at much lower redshifts, z < 2. We tackle the problem of the motion of inspiraling and merging black-hole binaries, which are among the most promising astrophysical sources of gravitational waves. We discuss a new approach for the two-body problem in general relativity, which makes it possible to study the transition between the adiabatic inspiral and the plunge, and which provides a first estimate of the gravitational waveform emitted during the late dynamical evolution of a binary black-hole system.