Davide Barbini, Alessio Notari, Oriol Pujolàs, Fabrizio Rompineve, Francisco Torrentí

Cosmic Domain Wall networks are among the most interesting sources of a stochastic Gravitational Wave (GW) background from the early Universe. We present a thorough analysis of their annihilation, with a focus on scenarios where the collapse is induced by a population bias, whereby one of two degenerate vacua is initially preferred over the other. Our state-of-the-art $3+1$ lattice field theory simulations in the expanding Universe reveal that the network decays around the temperature $T_\text{ann}\sim T_s\,\mathcal{B}_s^{0.8}$, where $\mathcal{B}_s$ quantifies the preference for one vacuum over the other at the onset of the scaling regime at the temperature $T_s$. Furthermore, we obtain the spectrum of GWs from such networks, and provide a detailed comparison with the alternative potential bias annihilation mechanism that relies on a small explicit symmetry breaking in the potential. En passant, we update results on the evolution of these networks and on their GWs, and clarify existing disagreements in the recent literature. Our results sharpen the phenomenological viability of spontaneously broken discrete symmetries, and provide GW spectra that Pulsar Timing Arrays (PTAs) and ground-based interferometers (LIGO-Virgo-KAGRA) can readily use in their searches for a cosmological GW background.