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 ∼ 2Hgw, where Hgw is the Hubble rate at the end of GW production, shortly after annihilation, (2) a doubly broken power law spectrum ∝ k-n, with initial slope n ∼ 0.5 after the main peak and n ∼ 1.8 at high f, while the low frequency region f < fp agrees with the causality behavior ∼ k3. Additionally, extending previous results, we find that GW production continues to be efficient until a value of the Hubble scale Hgw that is roughly an order of magnitude smaller than the naive estimate σH = ΔV, where σ is the wall tension and ΔV, 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.