We build an ultralight dark matter model with repulsive self-interactions, starting from a five-dimensional 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 four dimensions. 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 ${10}^{-12}\mathrm{eV}$ 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.

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• Cosmology
• Dark matter