  In order to accommodate the QCD axion as the dark matter (DM) in a model in
which the Peccei-Quinn (PQ) symmetry is broken before the end of inflation, a
relatively low scale of inflation has to be invoked in order to avoid bounds
from DM isocurvature fluctuations, $H_* \lesssim \mathcal{O}(10^9)\,$GeV. We
construct a simple model in which the Standard Model Higgs field is
non-minimally coupled to Palatini gravity and acts as the inflaton, leading to
a scale of inflation $H_* \sim 10^8\,$GeV. When the energy scale at which the
PQ symmetry breaks is much larger than the scale of inflation, we find that in
this scenario the required axion mass for which the axion constitutes all DM is
$m_0 \lesssim 0.05{\rm \,\mu eV}$ for a quartic Higgs self-coupling
$\lambda_\phi = 0.1$, which correspond to the PQ breaking scale $v_\sigma
\gtrsim 10^{14}\,$GeV and tensor-to-scalar ratio $r \sim 10^{-12}$. Future
experiments sensitive to the relevant QCD axion mass scale can therefore shed
light on the physics of the Universe before the end of inflation.
