  Conventional approaches to probing axions and axion-like particles (ALPs)
typically rely on a coupling to photons. However, if this coupling is extremely
weak, ALPs become invisible and are effectively decoupled from the Standard
Model. Here we show that such invisible axions, which are viable candidates for
dark matter, can produce a stochastic gravitational wave background in the
early universe. This signal is generated in models where the invisible axion
couples to a dark gauge boson that experiences a tachyonic instability when the
axion begins to oscillate. Incidentally, the same mechanism also widens the
viable parameter space for axion dark matter. Quantum fluctuations amplified by
the exponentially growing gauge boson modes source chiral gravitational waves.
For axion decay constants $f \gtrsim 10^{17}$ GeV, this signal is detectable by
either pulsar timing arrays or space/ground-based gravitational wave detectors
for a broad range of axion masses, thus providing a new window to probe
invisible axion models.
