Axion kinetic misalignment and parametric resonance from inflation

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 ${10}^8$ GeV $<f_a<{10}^{11}$ GeV can consistently produce axion dark matter. A significant portion of the allowed parameter space predicts rare kaon decays, $K_L\to ({\pi }^0+\text{missing energy})$, and/or suppression of structure formation on small scales.