Statistical physics of cosmological networks of string loops

We solve numerically the Boltzmann equation describing the evolution of a cosmic string network which contains only loops. In Minkowski space-time the equilibrium solution predicted by statistical mechanics is recovered, and we prove that this solution is stable to nonlinear perturbations provided that their energy does not exceed the critical energy for the Hagedorn transition. In expanding Einstein–de Sitter universes we probe the distribution of loops with a length much smaller than the horizon. Under the assumption that the length scales characteristic of the loop network scale, we discover stable scaling solutions for the energy density in loops, both in the radiation and matter dominated epochs. The shape of these solutions is very different in the two eras, with a much higher energy density in the radiation epoch, and a larger average loop length in the matter epoch. These results suggest that if the conditions for the formation of loop networks are indeed satisfied, these could, in principle, be good candidates for structure formation.