Statistical physics of cosmological networks of string loops - art. no. 103514

We solve numerically the Boltzmann equation describing the evolution of a c osmic 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 t hat their energy does not exceed the critical energy for the Hagedorn trans ition. 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 discove r stable scaling solutions for the energy density in loops, both in the rad iation and matter dominated epochs. The shape of these solutions is very di fferent 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 inde ed satisfied, these could, in principle, be good candidates for structure f ormation. [S0556-2821(99)06120-2].