TOPOLOGICAL DEFECTS AS SEEDS FOR ETERNAL INFLATION

We investigate the global structure of an inflationary universe both b y analytical methods and by computer simulations of stochastic process es in the early Universe. We show that the global structure of an infl ationary universe depends crucially on the mechanism of inflation. In the simplest models of chaotic inflation with the effective potentials phi(n) or e(alphaphi) the Universe looks like a sea of a thermalized phase, surrounding permanently self-reproducing inflationary domains. On the other hand, in the theories where inflation may occur near a lo cal extremum of the effective potential corresponding to a metastable state, the Universe looks like de Sitter space surrounding islands of a thermalized phase. A similar picture appears even if the state phi = 0 is unstable but the effective potential has a discrete symmetry, e. g., the symmetry phi --> = -phi. In this case the Universe becomes div ided into domains containing different phases (eta or -eta). These dom ains will be separated from each other by domain walls. However, unlik e ordinary domain walls often discussed in the literature, these domai n walls will inflate, and their thickness will exponentially grow. In the theories with continuous symmetries, inflation will generate expon entially expanding strings and monopoles surrounded by a thermalized p hase. Inflating topological defects will be stable, and they will unce asingly produce new inflating topological defects. This means that top ological defects may play a role of indestructible seeds for eternal i nflation.