Effect of reconnection probability on cosmic (super)string network density

Abstract

We perform numerical simulations of cosmic string evolution with intercommuting probability $P$ in the range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\le}P\ensuremath{\le}1$, both in the matter and radiation eras. We find that the dependence of the scaling density on $P$ is significantly different than the suggested $\ensuremath{\rho}\ensuremath{\propto}{P}^{\ensuremath{-}1}$ form. In particular, for probabilities greater than $P\ensuremath{\simeq}0.1$, $\ensuremath{\rho}(1/P)$ is approximately flat, but for $P$ less than this value it is well-fitted by a power-law with exponent ${0.6}_{\ensuremath{-}0.12}^{+0.15}$. This shows that the enhancement of string densities due to a small intercommuting probability is much less prominent than initially anticipated. We interpret the flat part of $\ensuremath{\rho}(1/P)$ in terms of multiple opportunities for string reconnections during one crossing time, due to small-scale wiggles. We also propose a two-scale model, which satisfactorily fits our results over the whole range of $P$ covered by the simulations.