Collisions of cosmic strings with chiral currents

We present an analytic study of cosmic superconducting chiral string collisions in Minkowski space, applying the kinematic constraints that arise from the relevant generalization of the Nambu-Goto action. In particular, we revisit the solution for chiral superconducting cosmic strings and demonstrate that Y junction production for such strings is possible. We consider the collision of chiral current-carrying straight strings and obtain the region in “angle-velocity” space that allows the production of string junctions. This study contributes to the understanding of the complex evolution of chiral superconducting string networks.

Figure 1

Collision of strings with currents, whose moving modes are represented by $F_i^{\prime }$ and ingoing/outgoing modes of strings are shown by vectors ${\mathbf{a}}_i^{\prime }$ and ${\mathbf{b}}_i^{\prime }$, respectively.

Figure 2

The left panel shows how the growth/decrease rate ${\dot{s}}_i$ for the string configurations is changing due to variations of current properties, represented by $F_I^{\prime }$ and ${\mathcal{D}}_I$. The right panel shows the value of the current $F_3^{\prime }$ generated on the junction for different values of $F_I^{\prime }$ and ${\mathcal{D}}_I$. All solid lines represent variation of $F_I^{\prime }$, with fixed ${\mathcal{D}}_I=0.5$, while all dashed lines represent variation of ${\mathcal{D}}_I$ with fixed $F_I^{\prime }=0.5$. These calculations are carried out for string tensions ${\mu }_1={\mu }_2=1$, ${\mu }_3=1.2$ when all vectors ${\mathbf{b}}_i^{\prime }$ are orthogonal.

Figure 3

The left panel shows how the growth/decrease rates ${\dot{s}}_i$ and the current $F_3^{\prime }$ for strings depend on $F_2^{\prime }$. The right panel shows the value of the angle $\beta$ between vectors ${\mathbf{b}}_2$ and ${\mathbf{b}}_3$. Calculations are carried out for string tensions ${\mu }_1=1$, ${\mu }_2=1.2$, ${\mu }_3=1.4$, while $F_1^{\prime }=0.2$, ${\mathcal{D}}_1=0.1$, and ${\mathcal{D}}_2=0.2$. The angles between vectors ${\mathbf{b}}_1$, ${\mathbf{b}}_2$ and ${\mathbf{b}}_1$, ${\mathbf{b}}_3$ are free and were chosen as $\pi /2$.

Figure 4

The left panel shows how the growth/decrease rates ${\dot{s}}_i$ for strings depend on ${\mathcal{P}}_2$ values. The right panel shows the value of ${\mathcal{P}}_3$ for the new (third) string. The thickness of lines shows variation of the value ${\mathcal{P}}_1$; i.e., the thinnest line corresponds to ${\mathcal{P}}_1=-0.4$ and the thickest one to ${\mathcal{P}}_1=0.4$ (dashed lines present the result for ${\mathcal{P}}_1=0.0$). Calculations are carried out for string tensions ${\mu }_1=1$, ${\mu }_2=1.2$, ${\mu }_3=1.4$. The vectors ${\mathbf{b}}_i$ are orthogonal to each other.

Figure 5

Range of parameters: velocity $\upsilon$ and angle $\alpha$, which allow the junction production (${\dot{s}}_3>0$) for the case when the heaviest string has the tension ${\mu }_3=1.4{\mu }_1=1.4{\mu }_2$. It is seen how the region of junction production depends on the value of colliding string currents (we also assumed ${\phi }_1={\phi }_2$).

Figure 6

Range of parameters, velocity $\upsilon$ and angle $\alpha$, which allow the junction production (${\dot{s}}_3>0$) for the case when string tensions are ${\mu }_1=1$, ${\mu }_2=1.2$, ${\mu }_3=1.4$. It is seen how the region of junction production depends on the value of colliding strings currents (we also assumed ${\phi }_1={\phi }_2$).