Thermal relaxation of an axion field produces a dark matter relic whose coherent and stochastic parts share one optical depth, yielding a subthermal momentum spectrum.
The one point probability distribution depends on the number of field quadratures, whereas gravitational structure depends on correlations between separated points
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Coherent and Stochastic Axion Dark Matter from Thermal Relaxation
Thermal relaxation of an axion field produces a dark matter relic whose coherent and stochastic parts share one optical depth, yielding a subthermal momentum spectrum.