  We consider cosmic loop production by long string interactions in
cosmological models with compact extra dimensions. In the case that the compact
manifold is not simply connected, we focus on the possibility of loops wrapping
around non-trivial cycles and becoming topologically trapped. Such loops,
denoted cycloops, behave like matter in the radiation era, posing a potential
monopole problem. We calculate the number distribution and the energy density
of these objects as functions of cosmic time and use them to study cosmological
constraints imposed on simple brane inflation models. For typical choices of
parameters we find that to avoid cycloop domination before the matter-radiation
transition, the strings must be unacceptably light, namely $G\mu<10^{-18}$,
unless some mechanism to dilute the cycloops is provided. By exploring the full
parameter space however, we are able to find models with $G\mu \sim 10^{-14}$,
which is marginally consistent with brane inflation. In such models the cycloop
could provide an interesting dark matter candidate.
