Near-Peak Spectrum of Gravitational Waves from Collapsing Domain Walls

Abstract: Cosmological domain walls appear in many well-motivated extensions to the standard model of particle physics. If produced, they quickly enter into a self-similar scaling regime, where they are capable of efficiently sourcing a stochastic background of gravitational waves. In order to avoid a cosmological catastrophe, they must also decay before their enormous energy densities can have adverse effects on background dynamics. Here, we provide a suite of lattice simulations to comprehensively study the gravitational wave signatures of the domain wall network during this decay phase. The domain walls are initially formed through spontaneous breaking of a $\mathbb{Z}_2$ symmetry, and subsequently decay through the action of a small bias term which causes regions of false vacuum to collapse. We find that gravitational waves are produced in abundance throughout this collapsing phase, leading to a shift in the peak frequency and increase in the overall amplitude of the spectrum by an $\mathcal{O}(100)$ factor when compared against simple analytic arguments. Importantly, we also find that the characteristic frequency of emitted gravitational waves increases as the network decays, which leads to a softening of the high frequency spectral index. This high frequency spectrum therefore carries key information related to the dynamics of the collapsing phase, and can be used to discriminate between different domain wall scenarios using upcoming data.