The era of precision cosmology allows us to test the composition of the dark matter. Mixed ultralight or fuzzy dark matter (FDM) is a cosmological model with dark matter composed of a combination of particles of mass $m\le {10}^{-20}\mathrm{eV}$, with an astrophysical de Broglie wavelength, and particles with a negligible wavelength sharing the properties of cold dark matter (CDM). In this work, we simulate cosmological volumes with a dark matter wave function for the ultralight component coupled gravitationally to CDM particles. We investigate the impact of a mixture of CDM and FDM in various proportions (0%, 1%, 10%, 50%, 100%) and for ultralight particle masses ranging over five orders of magnitude ($2.5\times {10}^{-25}\mathrm{eV}–2.5\times {10}^{-21}\mathrm{eV}$). To track the evolution of density perturbations in the nonlinear regime, we adapt the simulation code axionyx to solve the CDM dynamics coupled to a FDM wave function obeying the Schrödinger-Poisson equations. We obtain the nonlinear power spectrum and study the impact of the wave effects on the growth of structure on different scales. We confirm that the steady-state solution of the Schrödinger-Poisson system holds at the center of halos in the presence of a CDM component when it composes 50% or less of the dark matter but find no stable density core when the FDM accounts for 10% or less of the dark matter. We implement a modified friends-of-friends halo finder and find good agreement between the observed halo abundance and the predictions from the adapted halo model axionhmcode.

• Received 12 December 2023
• Accepted 7 January 2024

DOI:https://doi.org/10.1103/PhysRevD.109.043507