Small-scale structure on cosmic strings

We extend a linear-kink model of small-scale structure on cosmic strings and show how it is equivalent to an earlier two-scale model. By reconsidering the connection between the rate of loop production and the linear-kink density we correctly predict the build-up of small-scale structure currently seen in those simulations which neglect the gravitational back reaction. After including the gravitational back reaction we determine the full evolution of the small-scale structure, coupled to loop production and gravitational radiation. We confirm that the inclusion of the gravitational back reaction leads inevitably to the scaling of this structure, and that as many as ${10}^4$ kinks may persist on an horizon-sized segment of string.