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

We perform numerical simulations of cosmic string evolution with intercommuting probability $P$ in the range $5\times {10}^{-3}\le P\le 1$, both in the matter and radiation eras. We find that the dependence of the scaling density on $P$ is significantly different than the suggested $\rho \propto P^{-1}$ form. In particular, for probabilities greater than $P\simeq 0.1$, $\rho (1/P)$ is approximately flat, but for $P$ less than this value it is well-fitted by a power-law with exponent ${0.6}_{-0.12}^{+0.15}$. 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 $\rho (1/P)$ 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.

Figure 1

Dimensionless string density plotted against conformal time $\tau$ for a network with intercommuting probability $P=0.75$. Each curve corresponds to a different initial horizon to correlation length ratio. The asymptotic curves bracket the scaling solution, which can be estimated to be $\rho t^2/\mu ={3.6}_{-0.1}^{+0.2}$.

Figure 2

Dimensionless string scaling density plotted against the inverse intercommuting probability $1/P$, for matter and radiation era runs (1$\sigma$ errors displayed) . The constant slope part of the matter era data can be fitted by a power law with exponent ${0.6}_{-0.12}^{+0.15}$. The overall dependence of $\rho$ on $P$ is much weaker than the previously suggested $\rho \propto 1/P^2$ and $\rho \propto 1/P^2$ forms.

Figure 3

Dimensionless effective string tension $\tilde{\mu }$ plotted against physical distance (measured in units of physical time t) for matter era networks with $P=1,0.1,0.05$ and $0.01$. As $P$ is reduced, the effective tension increases signalling the accumulation of small-scale structure.

Figure 4

Scaling string density obtained from simulations (data points with errors) and from the analytic two-scale model (5, 6) (solid line). The fit is improved further (dashed line) by phenomenologically incorporating the dependence of the effective string tension $\tilde{\mu }$ on the reconnection probability $P$.