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New gravitational-wave templates for metastable cosmic strings: Loop breaking versus network collapse

Doa Hashemi Asl1,* and Kai Schmitz1,2,†

  • *Contact author: doa.hashemi@uni-muenster.de
  • †Contact author: kai.schmitz@uni-muenster.de
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Phys. Rev. D 114, 035010 – Published 5 August, 2026

DOI: https://doi.org/10.1103/y3qp-mtsb

Abstract

Metastable cosmic strings are a common prediction of grand unified theories and act as a source of a gravitational-wave background (GWB) that can explain the 2023 pulsar timing array (PTA) signal. In this paper, we revisit the GWB signal from metastable strings, emphasizing the need to carefully distinguish between two different timescales: (i) tLB, the timescale of loop breaking because of spontaneous monopole nucleation on closed string loops, and (ii) tNC, the timescale of network collapse when string segments attached to monopoles begin to enter the Hubble horizon. We discuss under which conditions these two timescales are similar or far apart from each other and illustrate the resulting consequences for the GWB signal. In doing so, we generalize the description of the GWB signal from metastable strings to a three-parameter model in terms of the string tension Gμ and the timescales tLB and tNC, which allows us to unify the modeling of standard metastable strings with what is known as quasistable strings. In the limit of a large tLB/tNC ratio, we, moreover, derive a compact analytical expression for the predicted GWB spectrum in excellent agreement with numerical results in the literature. We thus conclude that our new templates for the GWB spectrum from metastable strings can be readily used in the analysis of future PTA datasets.

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Phys. Rev. D 114, 035010– Published 5 August, 2026
  • Received 15 May 2026
  • Accepted 13 July 2026
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