We present a detailed discussion of the inflationary scenario in the context
of inhomogeneous cosmologies. After a review of the fundamental features
characterizing the inflationary model, as referred to a homogeneous and
isotropic Universe, we develop a generalization in view of including small
inhomogeneous corrections in the theory. A second step in our discussion is
devoted to show that the inflationary scenario provides a valuable dynamical
``bridge'' between a generic Kasner-like regime and a homogeneous and isotropic
Universe in the horizon scale. This result is achieved by solving the
Hamilton-Jacobi equation for a Bianchi IX model in the presence of a
cosmological space-dependent term. In this respect, we construct a
quasi-isotropic inflationary solution based on the expansion of the Einstein
equations up to first-two orders of approximation, in which the isotropy of the
Universe is due to the dominance of the scalar field kinetic term; the first
order of approximation corresponds to the inhomogeneous corrections and is
driven by the matter evolution. We show how such a quasi-isotropic solution
contains a certain freedom in fixing the space functions involved in the
problem. The main physical issue of this analysis corresponds to outline the
impossibility for the classical origin of density perturbations, due to the
exponential decay of the matter term during the de Sitter phase.Comment: 30 pages with cimento.cls, no figures, to appear on "Il Nuovo Cimento
B
