Nearest neighbour analysis as a new probe for fuzzy dark matter

Abstract: Fuzzy dark matter (FDM) is a promising candidate for dark matter, characterized by its ultra-light mass, which gives rise to wave effects at astrophysical scales. These effects offer potential solutions to the small-scale issues encountered within the standard cold dark matter (CDM) paradigm. In this paper, we investigate the large-scale structure of the cosmic web using FDM simulations, comparing them to CDM-only simulations and a simulation incorporating baryonic effects. Our study employs the nearest neighbor (NN) analysis as a new statistical tool for examining the structure and statistics of the cosmic web in an FDM universe. This analysis could capture the information absent in the two-point correlation functions. In particular, we analyze data related to the spherical contact, nearest neighbor distances, and the angle between the first and second nearest neighbors of halos. Specifically, we utilize probability distribution functions, statistical moments, and fitting parameters, as well as G(x), F(x), and J(x) functions to analyze the above data. Remarkably, the results from the FDM simulations differ significantly from the others across these analyses, while no noticeable distinction is observed between the baryonic and CDM-only simulations. Moreover, the lower FDM mass leads to more significant deviations from the CDM simulations. These compelling results highlight the efficiency of the NN analysis - mainly through the use of the J(x) function, $s_3$, $l_{3}$ and $a_4$ parameters - as a prominent new tool for investigating FDM on large scales and making observational predictions.