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

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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 =1/√ 2 and the characteristic length of non-interacting cosmic string networks scales as L ∝ a³/² (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 leads to a linear scaling solution with constant L H ≪ 1 (H is the Hubble parameter) and v 1/√ 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.