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A network of cosmic strings (CS), if present, would continue emittinggravitational waves (GW) as it evolves throughout the history of the Universe.This results in a characteristic broad spectrum making it a perfect source toinfer the expansion history. In particular, a short inflationary period causedby a supercooled phase transition would cause a drop in the spectrum atfrequencies corresponding to that event. However, the impact on the spectrum issimilar to the ones caused by an early matter-dominated era or from particleproduction, making it difficult to disentangle these different physicalorigins. We point out that, in the case of a short inflationary period, the GWspectrum receives an additional contribution from the phase transition itself.This leads to a characteristic imprint of a peak on top of a wide plateau bothvisible at future GW observatories.

Imprints of a Supercooled Phase Transition in the Gravitational Wave Spectrum from a Cosmic String network