Can inflationary axion fluctuations dominate over misalignment?

The relic abundance of light stable axion dark matter is usually set by misalignment. We study whether the inflationary fluctuations of the axion can dominate instead, and we follow the modes analytically through an instantaneous transition from de Sitter expansion to radiation domination, neglecting the axion mass during inflation and keeping it afterward. Since the energy density is quadratic in the field, a fluctuation-dominated abundance carries an isocurvature perturbation even when the mean displacement vanishes. For a canonical minimally coupled axion the spectrum is scale invariant, and fluctuation-dominated dark matter exceeds the Planck isocurvature limit by about eight orders of magnitude. An inflaton-dependent kinetic function or a nonminimal coupling to the Ricci scalar tilts the spectrum blue, moving the fluctuation power from CMB scales to small scales. Imposing the Planck limit at the pivot scale, we find that fluctuation-dominated dark matter with a constant kinetic slope requires the spectral tilt n η-1 0.27 and the axion mass m η 200 at H I=10 10, and n η-1 0.34 and m η 4.5, keV at H I=10 13. A kinetic function with a running slope lowers these masses to 1.4 and 0.7, eV, respectively. For the QCD axion, whose oscillations start late, we estimate that any single power-law spectrum blue enough to satisfy the pivot limit gives too little fluctuation abundance, and misalignment dominates.