Gravitational Wave Signatures from Warm Dark Energy

Motivated by some of the recent swampland conjectures, we study a model of dark energy, in which a quintessence axion slowly rolls in a steep potential due to its interactions with a U(1) or an SU(2) gauge field. The gauge fields produced by this interaction can generate a stochastic gravitational wave background with frequencies in the range $f \sim \left(10^{-16} - 10^{-14}\right)\; {\rm Hz}$. Gravitational waves in this range can in principle be probed by CMB spectral distortions. We show that the amplitude of the signal produced in this model is above the level for detectability only under very favourable choices of parameters.