We investigate the complementary information to be gained from inflationary gravitational wave (IGW) signals and searches for quantum chromodynamics (QCD) axion dark matter. We focus on postinflationary Peccei-Quinn (PQ) breaking axion models that are cosmologically safe. Recent work has shown that a greater number of such models exist. This is because the heavy quarks required for the color anomaly can provoke a period of heavy quark domination (HQD), which, through decay, dilutes the axion abundance. In this work we show for the first time that the axion dark matter mass can be as low as $m_a\sim {10}^{-8}\mathrm{eV}$ for models where the heavy quarks decay via dimension 6 terms. This is achieved by allowing the mass of the heavy quarks to differ from the axion decay constant, $m_Q\ne f_a$. Consequently, the observables that would distinguish between pre- and postinflationary PQ breaking, $m_a$ and the additional relativistic degrees of freedom $\mathrm{\Delta }{N}_{\mathrm{eff}}$, now become indiscernible. To solve this, we propose using blue-tilted IGWs to probe HQD. In scenarios where such a blue tilt is present, the enhanced GW signal allows future interferometers to place nontrivial constraints on the parameters $m_Q$ and $f_a$, thereby complementing haloscope searches. While some degeneracies with other parameters such as $m_Q$ remain, detectors such as Big Bang Observer and Einstein Telescope will be able to optimistically probe $f_a\gtrsim {10}^{14}\mathrm{GeV}$.

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• Cosmology
• Dark matter
• Gravitational wave detection
• Gravitational waves
• Particle dark matter
• Axions
• Gravitational wave detectors