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Fuzzy dark matter (FDM) is a dark matter candidate consisting of ultra-lightscalar particles with masses around $10^{-22} \mathrm{eV}/c^2$, a regime wherecold bosonic matter behaves as a collective wave rather than individualparticles. It has increasingly attracted attention due to its richphenomenology on astrophysical scales, with implications for the small-scaletensions present within the standard cosmological model, $\Lambda$CDM. Althoughconstraints on FDM are accumulating in many different contexts, very few havebeen verified by self-consistent numerical simulations. We present new largenumerical simulations of cosmic structure formation with FDM, solving the fullSchr\"odinger-Poisson (SP) equations using the AxiREPO code, which implements apseudo-spectral numerical method. Combined with our previous simulations, theyallow us to draw a four-way comparison of matter clustering, contrastingresults (such as power spectra) for each combination of initial conditions (FDMvs. CDM) and dynamics (SP vs. $N$-body). By disentangling the impact of initialconditions and non-linear dynamics, we can gauge the validity of approximatemethods used in previous works, such as ordinary $N$-body simulations with anFDM initial power spectrum. Due to the comparatively large volume achieved inour FDM simulations, we are able to measure the FDM halo mass function fromfull wave simulations for the first time, and compare to previous resultsobtained using analytic or approximate approaches. We find that, due to thecut-off of small-scale power in the FDM power spectrum, haloes are linked viacontinuous, smooth, and dense filaments throughout the entire simulation volume(unlike for the standard $\Lambda$CDM power spectrum), posing significantchallenges for reliably identifying haloes. We also investigate the densityprofiles of these filaments and compare to their CDM counterparts.

The halo mass function and filaments in full cosmological simulations with fuzzy dark matter