Hybrid model of condensate and particle dark matter: Linear perturbations in the hydrodynamic limit

We analyze perturbations of self-interacting, scalar field dark matter that contains modes in both a coherent condensate state and an incoherent particlelike state. Starting from the coupled equations for the condensate, the particles’ phase-space distribution, and their mutual gravitational potential, first derived from first principles in earlier work by the authors, we derive a hydrodynamic limit of two coupled fluids and study their linearized density perturbations in an expanding universe, also including particle pressure under an assumption for an equation of state consistent with the dynamical equations. We find that away from the condensate-only or particle-only limits, and for certain ranges of the parameters, such self-interacting mixtures can significantly enhance the density power spectrum above the standard linear $\mathrm{\Lambda }\mathrm{CDM}$ value at localized wave numbers, even pushing structure formation into the nonlinear regime earlier than expected in $\mathrm{\Lambda }\mathrm{CDM}$ for these scales. We also note that such mixtures can lead to degeneracies between models with different boson masses and self-coupling strengths, in particular, between self-coupled models and noncoupled fuzzy dark matter made up of heavier bosons. These findings open up the possibility of a richer phenomenology in scalar field dark matter models and could further inform efforts to place observational limits on their parameters.