New Massless Spectra from Cosmic String Cusps

TL;DR

This paper explores various shapes of cosmic string cusps, computes their gravitational-wave and axion spectra, and derives a general formula for cusp spectra, considering realistic corrections like backreaction and finite width.

Contribution

It introduces new cusp solutions with different shapes and derives a comprehensive spectrum formula, extending the standard Nambu-Goto model.

Findings

Different cusp shapes lead to varied GW spectra.

A general expression for cusp spectra is derived.

Realistic corrections impose high frequency cutoffs.

Abstract

In the standard picture of cosmic strings, cusps are generic features of Nambu-Goto loops where the string momentarily reaches the speed of light. They have a characteristic sharp profile, following $y \sim x^{2/3}$ in the $(x,y)$ plane, and produce strong gravitational-wave (GW) bursts with frequency-domain strain $\mathop{\tilde{\!\kappa}}(\omega) \propto \omega^{-4/3}$, making them key targets for current and future GW searches. However, under certain conditions, this generic picture can differ. We identify cusp solutions with different, including smooth, shapes, and compute their massless GW and axion spectra. We derive a general expression for all possible Nambu-Goto cusp spectra with the asymptotic form $\mathop{\tilde{\!\kappa}}(\omega) \propto \omega^{-n/(2n-1)} \omega^{-m/(2m-1)}$ where $n, m\geq 2$. We investigate the effect of realistic corrections to the Nambu-Goto description, such as those from backreaction and finite string width, which introduce a high frequency cutoff.