  Axion cold dark matter from standard misalignment typically requires a decay
constant $f_a~\gtrsim~10^{11}$ GeV. Kinetic misalignment and parametric
resonance easily allow lower values of $f_a$ when the radial Peccei-Quinn (PQ)
symmetry breaking field takes large initial values. Here, we consider the
effects of inflation on kinetic misalignment and parametric resonance. We
assume that the initial PQ field value is determined by quantum fluctuations,
and is set by the Hubble parameter during inflation, $H_I$, and the PQ field
mass. PQ field oscillations begin before or after the completion of reheating
after inflation at a temperature $T_R$. We determine the range of $f_a$ and the
inflationary parameters $(H_I, T_R)$ consistent with axion dark matter for a
quartic potential for the PQ field. We find that $4\times 10^8$ GeV $< f_a <
10^{11}$ GeV can consistently produce axion dark matter. A significant portion
of the allowed parameter space predicts rare kaon decays, $K_L \rightarrow
(\pi^0 + \rm{missing \; energy})$, and/or suppression of structure formation on
small scales.
