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The primordial irreducible gravitational-wave background due to quantumvacuum tensor fluctuations produced during inflation spans a large range offrequencies with an almost scale-invariant spectrum but is too low to bedetected by the next generation of gravitational-wave interferometers. We showhow this signal is enhanced by a short temporary kination era in thecosmological history (less than 10 e-folds), that can arise at any energy scalebetween a GeV and the inflationary scale $10^{16}$ GeV. We argue that suchkination era is naturally generated by a spinning axion before it gets trappedby its potential. It is usually assumed that the axion starts oscillatingaround its minimum from its initially frozen position. However, the earlydynamics of the Peccei-Quinn field can induce a large kinetic energy in theaxion field, triggering a kination era, either before or after the axionacquires its mass, leading to a characteristic peak in the primordialgravitational-wave background. This represents a smoking-gun signature of axionphysics as no other scalar field dynamics is expected to trigger such asequence of equations of state in the early universe. We derive the resultinggravitational-wave spectrum, and present the parameter space that leads to sucha signal as well as the detectability prospects, in particular at LISA,Einstein Telescope, Cosmic Explorer and Big Bang Observer. We show bothmodel-independent predictions and present as well results for two specificwell-motivated UV completions for the QCD axion dark matter where this dynamicsis built-in.

Revealing the Primordial Irreducible Inflationary Gravitational-Wave Background with a Spinning Peccei-Quinn Axion