Evolving ultralight scalars into non-linearity with Lagrangian perturbation theory

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