Gravitational radiation power spectrum of Garfinkle-Vachaspati cosmic string loops

We examine the power spectrum ${P}_{n}$ of the $n$th harmonic for Garfinkle-Vachaspati cosmic strings, which correspond to planar rectangular loops. While these loop trajectories are self-intersecting, a slightly perturbed non-self-intersecting form of these trajectories has been suggested as a generic end state of cosmic string loop fragmentation. We find that ${P}_{n}$ scales as ${n}^{\ensuremath{-}2}\mathrm{ln}n$, rather than the expected ${n}^{\ensuremath{-}2}$ for kink-kink collisions. This result is demonstrated analytically for even $n$ in square loops and numerically for all other cases. At lowest order, the effect of loop decays is to further enhance ${P}_{n}$ at large $n$ relative to its value at small $n$. The consequences for relic stochastic background radiation along with the caveats pertaining to our results are discussed.