Gravitational Radiation Power Spectrum of Garfinkle-Vachaspati Cosmic String Loops

TL;DR

This paper analyzes the power spectrum of harmonic modes in Garfinkle-Vachaspati cosmic string loops, revealing a logarithmic correction to the expected decay, with implications for gravitational wave backgrounds.

Contribution

It provides an analytical and numerical study showing the power spectrum scales as n^{-2} log n, differing from previous expectations, and discusses decay effects and cosmological implications.

Findings

Power spectrum scales as n^{-2} log n for cosmic string loops.

Loop decay enhances power spectrum at large n.

Results impact predictions of stochastic gravitational wave backgrounds.

Abstract

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 tractories 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 $n^{-2} \ln n$, rather than the expected $n^{-2}$ 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.