Cosmic string loops: large and small, but not tiny

Abstract

We develop an analytical model to study the production spectrum of loops in the cosmic string network. In the scaling regime, we find two different scales corresponding to large (one order below horizon) and small (few orders below horizon) loops. The very small (tiny) loops at the gravitational back reaction scale are absent, and thus, our model has no ultra-violet divergences. We calculate the spectrum of loops and derive analytical expressions for the positions and magnitudes of the small and large scale peaks. The small loops are produced by large bursts of similar loops moving with very high velocities in the same direction. We describe the shape of large loops, which would usually consist of few kinks and few cusps per oscillation cycle. We also argue that the typical size of large loops is set by the correlation length, which does not depend on the intercommutation probability p, while the interstring distance scales as p^{1/3}.