Gravitational waves from low-scale cosmic strings without scaling

TL;DR

This work analyzes gravitational-wave backgrounds from low-scale cosmic strings in a nonscaling framework where loops decay via both gravitational and particle channels, focusing on the fundamental oscillation mode which imposes a cutoff at $f_{ m cut}=2/l_{ m min}$. By introducing a length-dependent decay function $\mathcal{J}(l)$ to model particle radiation from kink–kink collisions and cusps, the authors derive analytic criteria for the existence of a cutoff and compute $l_{ m min}$ and $f_{ m cut}$ for NG, kinky, and cuspy loops; they then evaluate the resulting GWB spectrum exactly for nine benchmark points and provide analytical estimates for the peak frequency and amplitude. The results show that in many regions the nonscaling model reproduces scaling-model behavior, but particle decay can modify the low-to-high-scale boundary and shift the spectrum, including an oscillatory pattern above the peak associated with the cutoff. Overall, the study clarifies how particle radiation affects low-scale string GW signals, informs search strategies for future detectors like DECIGO and BBO, and helps distinguish low-scale from high-scale string scenarios through distinctive spectral features.

Abstract

Cosmic strings are predicted in many extensions of the Standard Model and constitute a plausible source of gravitational waves (GWs) from the early Universe. In a previous article arXiv:2405.10937v2, we pointed out that the GW spectrum from a population of string loops in the scaling regime can exhibit a sharp cutoff frequency associated with the fundamental oscillation mode of string loops. In this paper, we study the effect of particle decay due to kink-kink collisions and cusps on the GW spectrum in the nonscaling scenario introduced in Ref. arXiv:1911.12066. We find analytical conditions for the existence of a cutoff frequency in the fundamental spectrum and provide expressions for this frequency. In large regions of parameter space, our results in the nonscaling model turn out to be identical to those in the scaling model. Finally, we demonstrate how the spectrum changes when transitioning from the regime with a cutoff frequency to the regime without a cutoff frequency. Our analytical estimates are validated at qualitatively different benchmark points by comparing them with numerical spectra.

Figures (2)

• Figure 1: Plot of the two-dimensional parameter space spanned by string tension $G\mu$ and (initial) temperature $T$, i.e., the two parameters needed to describe the qualitatively different GWB spectra. Temperatures above $T_{\rm form}$ in Eq. \ref{['eq:Tform']} are excluded as in this region, strings have not formed yet, and we depict it as a black shaded region. Furthermore, we show $T_{\rm fric}$ in Eq. \ref{['eq:Tfric']} as a solid orange line and $T_{k(c)}$ as obtained from Eq. \ref{['eq:particledominancelength']} upon using Eq. \ref{['eq:TemperatureLoopLengthRelation']} as dashed dark-yellow and red-orange lines. In the left panel, we assume particle decay due to kink--kink collisions, in the right panel due to cusp formation with the respective temperatures $T_{\rm cut}^{k(c)}$ as obtained from Eq. \ref{['eq:InitialLoopLengthCriterion']} as blue lines. The parameter space of low-scale strings is the entire region that lies below these lines. We show the region above $T_{\rm cut}^{k(c)}$ with a grey shading to point at the absence of a cutoff frequency in the fundamental GWB spectrum. Moreover, we indicate the critical tensions $G\mu_{\rm crit}^{k(c)}$ as magenta dotted lines above and below which $T_{\rm cut}^{k(c)}$ approach the gravitational and particle decay dominated power-law behaviours given in Eqs. \ref{['eq:TemperatureCutNG']}, \ref{['eq:TemperatureCutKinks']}, and \ref{['eq:TemperatureCutCusps']}. The benchmark points specified in Tab. \ref{['tab:points']} are depicted by stars. Finally, we visualize the GWB peak amplitude determined from Eq. \ref{['eq:Omegapeak']} for each point in the parameter space in terms of a blue shading and corresponding contour lines in grey.
• Figure 2: Numerical GWB spectra based on the VOS equations for the long-string network for benchmark scenarios $1$ to $5$ (upper panels) and $1$, $1_A$ to $1_D$ (lower panels) as indicated in Fig. \ref{['fig:ParameterSpace']} and specified in Tab. \ref{['tab:points']}. The left and right columns assume particle radiation from kink--kink collisions and cusps, respectively. The dotted lines and shaded regions show the power-law-integrated sensitivity curves of future experiments (taken from Ref. Schmitz:2020syl).