2024MNRAS.52710538K

We investigate non-linear structure formation in the context of the fuzzy dark matter (FDM) model and compare it to the cold dark matter (CDM) model from a weak lensing perspective. Employing Eulerian perturbation theory (PT) up to fourth order, we calculate the tree-level matter trispectra and the one-loop matter spectra and bispectra from consistently chosen initial conditions. Furthermore, we conduct N-body simulations with CDM and FDM initial conditions to predict the non-linear matter power spectra. Subsequently, we derive the respective lensing spectra, bispectra, and trispectra for CDM and FDM within the framework of a Euclid-like weak lensing survey. In our analysis, we compute attainable cumulative signal-to-noise ratios and estimate χ²-functionals, aimed at distinguishing FDM from CDM at particle masses of m = 10^–21 eV, m = 10^–22 eV, and m = 10^–23 eV. Our results indicate that PT predictions are insufficient for distinguishing between the CDM and FDM models within the context of our simulated weak lensing survey for the considered particle masses. Assuming that N-body simulations overestimate late-time small-scale power in the FDM model, future weak lensing surveys may provide the means to discriminate between FDM and CDM up to a mass of m = 10^–23 eV. However, for stronger constraints on the FDM mass, observations of the local high-z universe may be more suitable.