Cosmological particle-in-cell simulations with ultralight axion dark
  matter
  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.
