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Gravitational wave bursts from cusps and kinks on cosmic strings

Thibault Damour, Alexander Vilenkin

TL;DR

This paper analyzes high-frequency gravitational wave bursts from cusps and kinks on cosmic strings, showing that the resulting GW background is strongly non-Gaussian with rare, loud bursts atop a confused Gaussian-like background. Using a left-right factorization of the string stress-energy tensor and a one-scale network model, the authors derive explicit cusp ($h^{\rm cusp}\propto G\mu\alpha^{2/3}f^{-1/3}$) and kink ($h^{\rm kink}\propto G\mu\alpha^{1/3}f^{-2/3}$) waveforms, compute their rates, and predict detectability by LIGO/VIRGO and LISA across a wide range of $G\mu$ values. A key contribution is the introduction of confusion noise, which captures overlapping bursts and yields revised pulsar timing constraints that are significantly weaker than the Gaussian rms background estimates, potentially allowing $G\mu$ up to $\sim 10^{-6}$ while still being consistent with data. The work highlights the importance of non-Gaussian statistics for string GW backgrounds and motivates improved simulations of cusp production and loop distributions, as well as targeted pulsar timing analyses that account for burstiness.

Abstract

The strong beams of high-frequency gravitational waves (GW) emitted by cusps and kinks of cosmic strings are studied in detail. As a consequence of these beams, the stochastic ensemble of GW's generated by a cosmological network of oscillating loops is strongly non Gaussian, and includes occasional sharp bursts that stand above the ``confusion'' GW noise made of many smaller overlapping bursts. Even if only 10% of all string loops have cusps these bursts might be detectable by the planned GW detectors LIGO/VIRGO and LISA for string tensions as small as $G μ\sim 10^{-13}$. In the implausible case where the average cusp number per loop oscillation is extremely small, the smaller bursts emitted by the ubiquitous kinks will be detectable by LISA for string tensions as small as $G μ\sim 10^{-12}$. We show that the strongly non Gaussian nature of the stochastic GW's generated by strings modifies the usual derivation of constraints on $G μ$ from pulsar timing experiments. In particular the usually considered ``rms GW background'' is, when $G μ\gaq 10^{-7}$, an overestimate of the more relevant confusion GW noise because it includes rare, intense bursts. The consideration of the confusion GW noise suggests that a Grand Unified Theory (GUT) value $ G μ\sim 10^{-6}$ is compatible with existing pulsar data, and that a modest improvement in pulsar timing accuracy could detect the confusion noise coming from a network of cuspy string loops down to $ G μ\sim 10^{-11}$. The GW bursts discussed here might be accompanied by Gamma Ray Bursts.

Gravitational wave bursts from cusps and kinks on cosmic strings

TL;DR

This paper analyzes high-frequency gravitational wave bursts from cusps and kinks on cosmic strings, showing that the resulting GW background is strongly non-Gaussian with rare, loud bursts atop a confused Gaussian-like background. Using a left-right factorization of the string stress-energy tensor and a one-scale network model, the authors derive explicit cusp () and kink () waveforms, compute their rates, and predict detectability by LIGO/VIRGO and LISA across a wide range of values. A key contribution is the introduction of confusion noise, which captures overlapping bursts and yields revised pulsar timing constraints that are significantly weaker than the Gaussian rms background estimates, potentially allowing up to while still being consistent with data. The work highlights the importance of non-Gaussian statistics for string GW backgrounds and motivates improved simulations of cusp production and loop distributions, as well as targeted pulsar timing analyses that account for burstiness.

Abstract

The strong beams of high-frequency gravitational waves (GW) emitted by cusps and kinks of cosmic strings are studied in detail. As a consequence of these beams, the stochastic ensemble of GW's generated by a cosmological network of oscillating loops is strongly non Gaussian, and includes occasional sharp bursts that stand above the ``confusion'' GW noise made of many smaller overlapping bursts. Even if only 10% of all string loops have cusps these bursts might be detectable by the planned GW detectors LIGO/VIRGO and LISA for string tensions as small as . In the implausible case where the average cusp number per loop oscillation is extremely small, the smaller bursts emitted by the ubiquitous kinks will be detectable by LISA for string tensions as small as . We show that the strongly non Gaussian nature of the stochastic GW's generated by strings modifies the usual derivation of constraints on from pulsar timing experiments. In particular the usually considered ``rms GW background'' is, when , an overestimate of the more relevant confusion GW noise because it includes rare, intense bursts. The consideration of the confusion GW noise suggests that a Grand Unified Theory (GUT) value is compatible with existing pulsar data, and that a modest improvement in pulsar timing accuracy could detect the confusion noise coming from a network of cuspy string loops down to . The GW bursts discussed here might be accompanied by Gamma Ray Bursts.

Paper Structure

This paper contains 20 sections, 121 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Emission of gravitational waves by cosmic strings in the local wave zone
  3. Waveform in the local wave zone
  4. Waveform emitted by a string loop
  5. Decay with frequency of the waveform: cusps, kinks and other singularities
  6. Logarithmic Fourier transform of GWB waveforms
  7. Gravitational wave bursts emitted by cusps and kinks
  8. Waveforms from cusps
  9. Waveforms from kinks
  10. Propagation of a gravitational wave burst in a cosmological spacetime
  11. Gravitational wave bursts from a cosmological network of string loops
  12. Simplified description of a string network
  13. Gravitational wave bursts from cusps
  14. Gravitational wave bursts from kinks
  15. Functional behaviour of $h^{\rm cusp}$ and $h^{\rm kink}$, and first comparison with planned GW detectors
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Gravitational wave amplitude of bursts emitted by cosmic string cusps (upper curves) and kinks (lower curve) in the LIGO/VIRGO frequency band, as a function of the parameter $\alpha = 50 \, G \, \mu$ (in a base-$10$ log-log plot). The upper curve assumes that the average number of cusps per loop oscillation is $c=1$. The middle curve assumes $c=0.1$. The lower curve gives the kink signal (assuming only one kink per loop). The horizontal dashed lines indicate the one sigma noise levels (after optimal filtering) of LIGO 1 (initial detector) and LIGO 2 (advanced configuration). The short-dashed line indicates the "confusion" amplitude noise of the stochastic GW background.
  • Figure 2: Gravitational wave amplitude of bursts emitted by cosmic string cusps (upper curves) and kinks (lower curve) in the LISA frequency band, as a function of the parameter $\alpha = 50 \, G \, \mu$ (in a base-$10$ log-log plot). The meaning of the three solid curves is as in Fig. \ref{['Fig1']}. The short-dashed slanted curve indicates the confusion noise. The lower long-dashed line indicates the one sigma noise level (after optimal filtering) of LISA.
  • Figure 3: Usual rms noise (upper short-dashed curve), confusion noise (lower short-dashed curve) and burst GW amplitude (solid line) emitted by cosmic string cusps, in the frequency band relevant for pulsar timing observations $(f_c = \dot N = 1 / (7 \, {\rm yr}))$. Here, we assumed $c=1$ and included the factor (\ref{['eq6.18']}) in the spatial density of loops.