Classical nontopological soliton configurations are considered within the theory of a complex scalar field with a gauged U(1) symmetry. Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically. The soliton configuration is such that inside the soliton the local U(1) symmetry is broken, the gauge field becomes massive, and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface. Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q matter in bulk form. We also briefly discuss solitons with fermions in a U(1) gauge theory.

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We show that under very general conditions any inhomogeneous cosmological model with a positive cosmological constant that can be described in a synchronous reference system will tend asymptotically in time towards the de Sitter solution, so making the problem of initial conditions less severe. The implications for inflationary scenarios are examined, and it is found that after inflation the Universe stays isotropic and homogeneous for a very long time.

Exact analytical solutions of Einstein's equations are found for a spherically symmetric inhomogeneous metric in the presence of a massless scalar field with a flat potential. The process of isotropization and homogenization is studied in detail. It is found that the time dependence of the metric becomes de Sitter for large times. Two cases are studied. The first deals with a homogeneous scalar field, while the second with a spherically symmetric inhomogeneous scalar field. In the former case the metric is of the Robertson-Walker form,

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