Repulsive dark matter from Hosotani mechanism

We build an ultralight dark matter model with repulsive self-interactions, starting from a 5D action that only includes a $U(1)$ gauge field and several massive and charged free fermions. The dark matter scalar field corresponds to the fifth component of the gauge field, after compactification to 4D. Although the single-fermion case only leads to attractive self-interactions, two fermions can already give rise to repulsive self-interactions, thanks to a Scherk-Schwarz twist around the fifth dimension. We check the observational and theoretical self-consistency of this scenario, from the inflation stage to the current time. We find that large ranges of model parameters are allowed. For scalar masses below $10^{-12}$ eV the self-interactions are negligible and the model behaves as fuzzy dark matter. For higher masses the repulsive self-interactions govern the formation of solitons of astrophysical size. Larger sizes require a large initial misalignment or small masses in the fuzzy dark matter regime.