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

Fuzzy dark matter (FDM) is a dark matter candidate consisting of ultra-light 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. It has increasingly attracted attention due to its rich phenomenology on astrophysical scales, with implications for the small-scale tensions present within the standard cosmological model, $\Lambda$CDM. 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 Schr\"odinger-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 (FDM vs. CDM) and dynamics (SP vs. $N$-body). By disentangling the impact of initial conditions and non-linear dynamics, 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 find that, due to the cut-off of small-scale power in the FDM power spectrum, haloes are linked via continuous, smooth, and dense filaments throughout the entire simulation volume (unlike for the standard $\Lambda$CDM power spectrum), posing significant challenges for reliably identifying haloes. We also investigate the density profiles of these filaments and compare to their CDM counterparts.