Quantum fluctuations of axions

We study the time evolution of the quantum fluctuations of the axion field for both the QCD axion as well as axions arising in the context of supergravity and string theories. We explicitly keep track not only of the coherently oscillating zero momentum mode of the axion but also of the higher non-zero momentum modes using the full axion potential. The full axion potential makes possible two kinds of instabilities: spinodal instabilities and parametric resonance instabilities. The presence of either of these instabilities can lead to a quasi-exponential increase in the occupation of non-zero momentum modes and the build-up of the quantum fluctuations of the axions. If either of these becomes a significant effect then axions would no longer be a suitable cold dark matter candidate. Our results confirm the conventional wisdom that these effects are not significant in the setting of an expanding FRW universe and hence axions are indeed cold dark matter candidates. copyright 1998 The American Physical Society