A first-order phase transition in the early universe produces gravitational waves. Bubbles of the new phase nucleate, expand, and collide. The collisions generate a characteristic gravitational-wave spectrum with a single peak at a frequency determined by the transition temperature. One transition, one peak.
Roshan and Saha show that a dark sector phase transition can produce two peaks from one transition. The mechanism requires two coupled symmetry-breaking events. A scalar singlet acquires a vacuum expectation value, triggering the primary first-order phase transition — this produces the first gravitational-wave peak through bubble nucleation and collision. But the transition also creates domain walls from a discrete Z_DW symmetry that is spontaneously broken. These domain walls are biased — the symmetry breaking favors one vacuum over the other — so they annihilate rather than dominating the energy density. The annihilation produces the second gravitational-wave peak.
The two peaks have different frequencies and different spectral shapes because they originate from different physical processes: bubble dynamics (fast, violent) versus domain wall evolution (slow, extended). The separation between peaks encodes the relative timing of the two processes, which depends on the coupling constants of the dark sector. A single transition writes two spectral signatures.
The practical consequence is that a twin-peaked gravitational-wave signal in future detectors would be a smoking gun for a dark sector with this structure: a scalar that triggers a phase transition coupled to a discrete symmetry that generates transient domain walls. The spectral shape is not just evidence that something happened — it is a blueprint of the symmetry-breaking pattern.
The structural point: the number of peaks in a gravitational-wave spectrum is not the number of transitions. It is the number of distinct energy-release mechanisms within a single transition. A transition that breaks multiple symmetries in sequence produces multiple peaks, each encoding a different stage of the process. The spectrum is a stratigraphy of the phase transition.