Scaling and small-scale structure in cosmic string networks

Abstract

We examine the scaling properties of an evolving network of strings in Minkowski spacetime and study the evolution of length scales in terms of a three-scale model proposed by Austin, Copeland, and Kibble (ACK). We find good qualitative and some quantitative agreement between the model and our simulations. We also investigate small-scale structure by altering the minimum allowed size for loop production ${E}_{c}.$ Certain quantities depend significantly on this parameter: for example, the scaling density can vary by a factor of 2 or more with increasing ${E}_{c}.$ Small-scale structure as defined by ACK disappears if no restrictions are placed on loop production, and the fractal dimension of the string changes smoothly from 2 to 1 as the resolution scale is decreased. Loops are nearly all produced at the lattice cutoff. We suggest that the lattice cutoff should be interpreted as corresponding to the string width, and that in a real network loops are actually produced with this size. This leads to a radically different string scenario, with particle production rather than gravitational radiation being the dominant mode of energy dissipation. At the very least, a better understanding of the discretization effects in all simulations of cosmic strings is called for.