In realistic metastable cosmic string scenarios, thermal fluctuations on the string prevent endpoint monopoles from reaching relativistic speeds, so string segments contribute negligibly to the gravitational wave background.
Vilenkin, COSMOLOGICAL EVOLUTION OF MONOPOLES CONNECTED BY STRINGS, Nucl
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Do Cosmic String Segments Emit Gravitational Waves?
In realistic metastable cosmic string scenarios, thermal fluctuations on the string prevent endpoint monopoles from reaching relativistic speeds, so string segments contribute negligibly to the gravitational wave background.