ON STRING TUNNELING IN POWER-LAW INFLATIONARY UNIVERSES

We consider the evolution of circular string loops in power law expand ing universes represented by a spatially flat Friedman-Robertson-Walke r metric with scale factor a(t) is-proportional-to t(p), where t is th e cosmic time and p greater-than-or-equal-to 0. Our main result is the existence of a ''magic'' power p(m) = 3 + 2 square-root 2. In spaceti mes with p < p(m) a circular string expands either forever or to a max imal radius and then contracts until it collapses into a point (black hole). For p greater-than-or-equal-to p(m), however, we find additiona l types of solutions. They include configurations which contract from a positive initial radius to a minimal one and then expand forever. Th eir existence we interpret as an indication for the presence of a fini te potential barrier. Equivalently the new solutions signal string nuc leation and tunnelling, phenomena recently shown to occur in de Sitter space.