Scaling solutions in cosmic-string networks

The evolution of a cosmic-string network is examined in terms of two length scales: $\xi$, related to the long-string density, and $\xi$, the persistence length along the left- or right-moving string, respectively. Previous work is extended by allowing for the dependence of some of the parameters on these scales. The changes have some dramatic effects. As before an important role is played by the parameter $q$ describing the relative kinkiness of a loop as compared to a section of string of the same length. We show that scaling solutions, in which both $\xi$ and $\xi$ are of similar length, both proportional to the horizon size, exist for all values of $q$. However, for small values of $q$ these solutions are unstable, so the scaling solution will actually be reached only for $q$ larger than some critical value of order 2. The results are compared with those of Allen and Caldwell and the possibility that scaling has not in fact been reached is briefly discussed.