Zipping and unzipping of cosmic string loops in collision

In this paper the collision of two cosmic string loops is studied. After collision junctions are formed and the loops are entangled. We show that after their formation the junctions start to unzip and the loops disentangle. This analysis provides a theoretical understanding of the unzipping effect observed in numerical simulations of a network of cosmic strings with more than one type of cosmic strings. The unzipping phenomena have important effects in the evolution of cosmic string networks when junctions are formed upon collision, such as in a network of cosmic superstrings.

Figure 1

A schematic view of the loops at the time of collision (left) and after collision (right). The arrows in the right figure indicate the directions in which the ${\sigma }_i$ coordinate increases. We use the convention that on a loop ${\sigma }_i$ runs counterclockwise. There are four junctions and eight kinks in total.

Figure 2

Here the numerical solutions for $s_3^B(t)$ (left) and $s_3^D$ (right) are plotted for $\gamma =1.1$, ${\mu }_1/{\mu }_3=0.7$, $\alpha =\pi /8$ and $t_0=0.1$ in units where $R_0=1$. The unzipping for junction B (D) happens when $s_3^B$ ($s_3^D$) reaches a maximum (minimum) value. In this example, the loop disentanglement happens at $t_f\simeq 1.4$ before the loops shrink at $t_{\mathrm{shrink}}\simeq 1.7$.