One-dimensional fuzzy dark matter models: Structure growth and asymptotic dynamics

This paper investigates the feasibility of simulating fuzzy dark matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in (1+1)-dimensional space time, that—under well controlled system conditions—is capable of realizing important aspects of the full-fledged (3+1)-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal (3+1)-Schrödinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for nonexpanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modeling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them.