In superfluid dark matter, the charge tied to the chemical potential is not conserved, so the chemical potential is only an approximation valid on timescales much shorter than 10^8 years; the paper gives the correct prescription and a two-field alternative.
Effective gravitational interactions of dark matter axions
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abstract
We investigate the structure of gravitational self-interactions of coherently oscillating axions in the general relativistic framework. A generic action for a massive scalar field in the Friedmann-Robertson-Walker background is first introduced based on the effective field theory approach to cosmological perturbations. Using the obtained setup, we evaluate the effective gravitational interaction of the massive scalar field, i.e. scalar quartic interactions mediated by metric perturbations. Applying the results to the system of dark matter axions, we estimate their self-interaction rate and discuss its implications for the axion Bose-Einstein condensate dark matter scenario. Leading contributions for the gravitational interactions of axions are given by the process mediated by the dynamical graviton field, which is essentially the Newtonian potential induced by fluctuations of the background fluids. We find that it leads to the same order of magnitude for the interaction rate of dark matter axions in the condensed regime, compared with the results of previous studies using the Newtonian approximation.
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The role of the chemical potential in coupling superfluid dark matter to baryons
In superfluid dark matter, the charge tied to the chemical potential is not conserved, so the chemical potential is only an approximation valid on timescales much shorter than 10^8 years; the paper gives the correct prescription and a two-field alternative.