Gravitational self-interactions of cosmic strings

We study the gravitational back reaction of local cosmic-string loops as they shrink due to gravitational radiation. We chart the evolution of the shape and radiation rate of the loops. Cusps survive gravitational back reaction, but are weakened. Asymmetric string trajectories radiate momentum and hence undergo a rocket effect, but the effect is not very significant. Typically, a string loop's center-of-mass velocity is changed by $\Delta v\sim 0.1c$. Trajectories that have few modes and that are non-self-intersecting remain so almost until the end of the string's lifetime. We also study highly kinky loops. Small kinks decay very quickly, the decay time for a kink of size $l$ being given by $t{\mathrm{}\left(l\right)\mathrm{}}_{\mathrm{decay}}\sim {\left({\Gamma }_{\mathrm{kink}}G\mu \right)}^{-1\mathrm{}}l$, where ${\Gamma }_{\mathrm{kink}}\sim 50$. We argue that this limits the smallest relevant structures on long strings in networks to a fraction (${\Gamma }_{\mathrm{kink}}G\mu$) of the size of the horizon, and that this will also set the scale for loops produced off a network. This, coupled with results from string network simulations and millisecond-pulsar constraints, limits the string tension to $G\mu <2\mathrm{}\times {10}^{-5\mathrm{}}$. This is far from ruling out the cosmic-string scenario of galaxy formation.