Scaling laws for weakly interacting cosmic (super)string and p-brane networks

In this paper we find new scaling laws for the evolution of p-brane networks in N + 1-dimensional Friedmann-Robertson-Walker universes in the weakly interacting limit, giving particular emphasis to the case of cosmic superstrings (p = 1) living in a universe with three spatial dimensions (N = 3). In particular, we show that, during the radiation era, the root-mean-square velocity is (v) over bar = 1/root 2 and the characteristic length of non-interacting cosmic string networks scales as L proportional to a(3/2) (a is the scale factor), thus leading to string domination even when gravitational backreaction is taken into account. We demonstrate, however, that a small non-vanishing constant loop chopping efficiency parameter (c) over tilde leads to a linear scaling solution with constant LH << 1 (H is the Hubble parameter) and (v) over bar similar to 1/root 2 in the radiation era, which may allow for a cosmologically relevant cosmic string role even in the case of light strings. We also determine the impact that the radiation-matter transition has on the dynamics of weakly interacting cosmic superstring networks.