  We discuss production of QCD axion dark matter in a novel scenario, which
assumes time-varying scale of Peccei-Quinn symmetry breaking. The latter
decreases as the Universe's temperature at early times and eventually
stabilises at a large constant value. Such behavior is caused by the portal
interaction between the complex field carrying Peccei-Quinn charge and a
Higgs-like scalar, which is in thermal equilibrium with primordial plasma. In
this scenario, axions are efficiently produced during the parametric resonance
decay of the complex Peccei-Quinn field, relaxing to the minimum of its
potential in the radiation-dominated stage. Notably, this process is not
affected by the Universe's expansion rate and allows to generate the required
abundance of dark matter independently of an axion mass. Phenomenological
constraints on the model parameter space depend on the number density of radial
field fluctuations, which are also generically excited along with axions, and
the rate of their thermalization in the primordial plasma. For the ratio of
radial field and axion particles number densities larger than $\sim 0.01$ at
the end of parametric resonance decay, the combination of cosmological and
astrophysical observations with the CAST limit confines the Peccei-Quinn scale
to a narrow range of values $\sim 10^{8}~\mbox{GeV}$, - this paves the way for
ruling out our scenario with the near future searches for axions.
