  We consider the evolution of circular string loops in power law expanding
universes represented by a spatially flat Friedman-Robertson-Walker metric with
scale factor $a(t)\propto t^p$ where $t$ is the cosmic time and $p\geq 0$. Our
main result is the existence of a "magic" power $p_m=3+2\sqrt{2}$. In
spacetimes with $p<p_m$ a circular string expands either forever or to a
maximal radius and then contracts until it collapses into a point (black hole).
For $p>p_m$, however, we find additional types of solutions. They include
configurations which contract from a positive initial radius to a minimal one
and then expand forever. Their existence we interpret as an indication for the
presence of a finite potential barrier. Equivalently the new solutions signal
string nucleation and tunneling, phenomena recently shown to occur in de Sitter
space.
