Multi-peaked spectra of the primordial gravitational waves are considered as a phenomenologically relevant source of information about the dynamics of sequential phase transitions in the early Universe. In particular, such signatures trace back to specific patterns of the first-order electroweak phase transition in the early Universe occurring in multiple steps. Such phenomena appear to be rather generic in multi-scalar extensions of the Standard Model. In a particularly simple extension of the Higgs sector, we have identified and studied the emergence of sequential long- and short-lasting transitions as well as their fundamental role in generation of multi-peaked structures in the primordial gravitational-wave spectrum. We discuss the potential detectability of these signatures by the proposed gravitational-wave interferometers.
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