Evolving Ultralight Scalars into Non-Linearity with Lagrangian
  Perturbation Theory
  Many models of high energy physics suggest that the cosmological dark sector
consists of not just one, but a spectrum of ultralight scalar particles with
logarithmically distributed masses. To study the potential signatures of low
concentrations of ultralight axion (also known as fuzzy) dark matter, we modify
Lagrangian perturbation theory (LPT) by distinguishing between trajectories of
different dark matter species. We further adapt LPT to include the effects of a
quantum pressure, which is necessary to generate correct initial conditions for
ultralight axion simulations. Based on LPT, our modified scheme is extremely
efficient on large scales and it can be extended to an arbitrary number of
particle species at very little computational cost. This allows for computation
of self-consistent initial conditions in mixed dark matter models.
Additionally, we find that shell-crossing is delayed for ultralight particles
and that the deformation tensor extracted from LPT can be used to identify the
range of redshifts and scales for which the Madelung formalism of fuzzy dark
matter is a reliable approximation.
