ABSTRACT Fuzzy dark matter (FDM) is a dark matter candidate consisting of ultralight scalar particles with masses around $10^{-22}\, \mathrm{eV}/c^2$, a regime where cold bosonic matter behaves as a collective wave rather than individual particles. Although constraints on FDM are accumulating in many different contexts, very few have been verified by self-consistent numerical simulations. We present new large numerical simulations of cosmic structure formation with FDM, solving the full Schrödinger–Poisson (SP) equations using the AxiREPO code, which implements a pseudo-spectral numerical method. Combined with our previous simulations, they allow us to draw a four-way comparison of matter clustering, contrasting results (such as power spectra) for each combination of initial conditions (ICs; FDM versus cold dark matter, CDM) and dynamics (SP versus N-body). By disentangling the impact of ICs and non-linear dynamics in this manner, we can gauge the validity of approximate methods used in previous works, such as ordinary N-body simulations with an FDM initial power spectrum. Due to the comparatively large volume achieved in our FDM simulations, we are able to measure the FDM halo mass function from full wave simulations for the first time, and compare to previous results obtained using analytic or approximate approaches. We also investigate the density profiles of these filaments and compare to their ΛCDM counterparts.

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