The Spectrum of Gravitational Waves from Annihilating Domain Walls

Abstract

Networks of cosmic domain walls can form in the early Universe as a consequence of the spontaneous breaking of discrete symmetries. We study the production of a cosmological background of gravitational waves (GWs) from such networks, when they annihilate due to a small explicit symmetry breaking term. Averaging over several 3+1-dimensional high-resolution lattice field simulations, we obtain a GW spectrum with the following characteristics: (1) a broad asymmetric peak, roughly located at frequency (at the time of emission) $f\sim 2H_{\mathrm{gw}}$, where $H_{\mathrm{gw}}$ is the Hubble rate at the end of GW production, shortly after annihilation, (2) a doubly broken power law spectrum $\propto k^{-n}$, with initial slope $n\sim 0.5$ after the main peak and $n\sim 1.8$ at high $f$, while the low frequency region $f<f_p$ agrees with the causality behavior $\sim k^3$. Additionally, extending previous results, we find that GW production continues to be efficient until a value of the Hubble scale $H_{\text{g}w}$ that is roughly an order of magnitude smaller than the naive estimate $\sigma H=\Delta V$, where $\sigma$ is the wall tension and $\Delta V$ the size of the symmetry breaking term, thereby leading to a $O(100)$ larger GW signal. We find such results to be robust when changing the shape of the scalar field potential or including a time-dependent symmetry breaking term. Our findings have important implications for GW searches, especially in light of the reported evidence for a stochastic GW background in Pulsar Timing Array data.

Comments: 16 pages + appendices, 20 figures. It includes new results on scalar spectra for different bias sizes. It matches version published in JCAP