Imprint of domain wall annihilation on induced gravitational waves

Domain wall annihilation can leave a distinctive imprint on the induced gravitational wave spectrum. During annihilation, most of the domain wall energy transforms into the scalar field responsible for the initial $\mathbb{Z}_2$ symmetry breaking that created the walls, along with any coupled species. If the produced scalar is sufficiently long-lived, its delayed decay drives an early matter-dominated phase following domain wall annihilation, significantly amplifying induced gravitational waves from primordial perturbations. The subsequent transition to radiation domination dilutes the domain wall contribution through entropy injection while preserving the enhanced induced signal. This creates a gravitational wave spectrum with two distinct peaks detectable across complementary frequency bands. We explore the observable parameter space and demonstrate how multi-band detection can probe early universe symmetry breaking.