  In this paper, we consider dynamical Chern-Simons gravity with the
identification of the scalar field coupled though the Pontryagin density with
the axion dark matter, and we discuss the effects of the parametric resonance
on gravitational waves (GWs). When we consider GWs in a coherently oscillating
axion cloud, we confirm that significant resonant amplification of GWs occurs
in a narrow frequency band, and the amplification is restricted to the late
epoch after the passage of the incident waves. We also identify the condition
that an axion cloud spontaneously emits GWs. Once we take into account the
randomness of the spatial phase distribution of the axion oscillations, we find
that the amplification is suppressed compared with the coherent case, but
significant amplification of GWs can still occur. We also examine whether or
not the amplification of GWs is possible in the present universe, taking into
account the history of the universe. We find that resonant amplification is
difficult to be tested from GW observations in the standard scenario of the
axion DM model, in which the axion is the dominant component of DM. However,
there is some parameter window in which the resonant amplification of GWs might
be observed, if the axion is subdominant component of DM, and the axion cloud
formation is delayed until the Hubble rate becomes much smaller than the axion
mass.
