Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms

TL;DR

This paper introduces a method to incorporate small-scale structures into cosmic strings, explores how these structures affect cusp shapes, and analyzes their impact on gravitational waveforms, showing that waveforms are generally preserved but smoothed.

Contribution

The paper presents a novel method for adding small-scale structure to cosmic strings and analyzes its effects on cusp shapes and gravitational wave signals.

Findings

Small-scale structure influences cusp shapes and loop formation.

Gravitational waveforms remain largely unchanged but are smoothed by small-scale structure.

Cusp waveforms are robust against small-scale modifications.

Abstract

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.