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

TL;DR

This paper derives new scaling laws for weakly interacting p-brane networks, especially cosmic superstrings, showing how their velocities and characteristic lengths evolve in different cosmological eras, with implications for their cosmological relevance.

Contribution

It introduces novel scaling laws for p-brane networks in higher-dimensional universes, emphasizing the effects of weak interactions and the radiation-matter transition on cosmic superstring dynamics.

Findings

Non-interacting string networks have characteristic length scaling as $a^{3/2}$ during radiation era.

A small loop chopping efficiency leads to linear scaling with constant $L H$.

Cosmic superstrings can have a cosmologically relevant role even if light, due to weak interactions.

Abstract

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 ${\bar v} =1/{\sqrt 2}$ and the characteristic length of non-interacting cosmic string networks scales as $L \propto a^{3/2}$ ($a$ 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 $\tilde c$ leads to a linear scaling solution with constant $L H \ll 1$ ($H$ is the Hubble parameter) and ${\bar v} \sim 1/{\sqrt 2}$ 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.