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Domain wall evolution beyond quartic potentials: The Sine-Gordon potential and Christ-Lee potentials

R. Heilemann1,2,3,*, M. C. Rosa1,†, J. R. C. C. C. Correia4,‡, and C. J. A. P. Martins1,3,§

  • *Contact author: Ricarda.Heilemann@astro.up.pt
  • †Contact author: manuel.crosa@gmail.com
  • ‡Contact author: jose.correia@helsinki.fi
  • §Contact author: Carlos.Martins@astro.up.pt
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Phys. Rev. D 111, 123550 – Published 25 June, 2025

DOI: https://doi.org/10.1103/rh2q-w1f6

Abstract

Domain walls are the simplest type of topological defects formed at cosmological phase transitions, and one of the most constrained. Their studies typically assume a quartic double well potential, but this model is not fully representative of the range of known or plausible particle physics models. Here, we study the cosmological evolution of domain walls in two other classes of potentials. The Sine-Gordon potential allows several types of walls, interpolating between different pairs of minima (which demands specific numerical algorithms to separately measure the relevant properties of each type). The Christ-Lee potentials parametrically interpolates between sextic and quartic behavior. We use multiple sets of simulations in two and three spatial dimensions, for various cosmological epochs and under various choices of initial conditions, to discuss the scaling properties of these networks. In the Sine-Gordon case, we identify and quantify deviations from the usual scaling behavior. In the Christ-Lee case, we discuss conditions under which walls form (or not) and quantify how these outcomes depend on parameters such as the energy difference between the false and true vacua and the expansion rate of the Universe. Various biased initial conditions are also addressed in the Appendixes. Finally, we briefly comment on the possible cosmological implications of our results.

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Phys. Rev. D 111, 123550– Published 25 June, 2025
  • Received 11 December 2024
  • Accepted 10 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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