Abstract
We study cosmological structure formation with ultralight axion dark matter, or "fuzzy dark matter (FDM), using a particle-mesh scheme to account for the quantum pressure arising in the Madelung formulation of the Schr\"odinger-Poisson equations. Subpercent-level energy conservation and correct linear behavior are demonstrated. Whereas the code gives rise to the same core-halo profiles as direct simulations of the Schr\"odinger equation, it does not reproduce the detailed interference patterns. In cosmological simulations with FDM initial conditions, we find a maximum relative difference of O($10\%$) in the power spectrum near the quantum Jeans length compared to using a standard N-body code with identical initial conditions. This shows that the effect of quantum pressure during nonlinear structure formation cannot be neglected for precision constraints on a dark matter component consisting of ultralight axions.
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