Nonlinear dynamics of cosmic strings with nonscaling loops

At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l_min. To understand the late time behavior we propose a very simple analytical model of strings with a nonscaling population of loops. The complicated nonlinear dynamics is described by only a single parameter N∼2/(1-C(l_min)) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length ξ∼t/N2 and the cross-correlation length χ∼t/N. At the onset of evolution N∼10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than l_min.