Self-intersections and gravitational properties of chiral cosmic strings in Minkowski space

Chiral cosmic strings are naturally produced at the end of D-term inflation and they may have interesting cosmological consequences. As was first proved by Carter and Peter, the equations of motion for chiral cosmic strings in Minkowski space are integrable (just as for Nambu-Goto strings). Their solutions are labeled by a function $k(\sigma - t)$ where $t$ is time and $\sigma$ is the invariant length along the string, and the constraints on $k$, which determines the charge on the string, are that $0 \leq k^2 \leq 1$. We review the origin of this parameter and also discuss some general properties of such strings which can be deduced from the equations of motion. The metric around infinite chiral strings is then constructed in the weak field limit, and studied as a function of $k$. We also consider the angular momentum of circular chiral loops, and extend previous work to consider the evolution and self-intersection properties of a more general family of chiral cosmic string loops for which $k^2(\sigma-t)$ is not constant.