  We investigate the length of the period of validity of a classical
description for the cosmic axion field. To this end, we first show that we can
understand the oscillating axion solution as expectation value over an
underlying coherent quantum state. Once we include self-interaction of the
axion, the quantum state evolves so that the expectation value over it starts
to deviate from the classical solution. The time-scale of this process defines
the quantum break-time. For the hypothetical dark matter axion field in our
Universe, we show that quantum break-time exceeds the age of the Universe by
many orders of magnitude. This conclusion is independent of specific properties
of the axion model. Thus, experimental searches based on the classical
approximation of the oscillating cosmic axion field are fully justified.
Additionally, we point out that the distinction of classical nonlinearities and
true quantum effects is crucial for calculating the quantum break-time in any
system. Our analysis can also be applied to other types of dark matter that are
described as classical fluids in the mean field approximation.
