A weak lensing perspective on nonlinear structure formation with fuzzy dark matter

We investigate nonlinear structure formation in the fuzzy dark matter (FDM) model in comparison to cold dark matter (CDM) models from a weak lensing perspective using perturbative methods. We use Eulerian perturbation theory (PT) up to fourth order to compute the tree-level matter trispectrum and the one-loop matter spectrum and bispectrum from consistently chosen initial conditions. In addition, we predict the non-linear matter power spectra using $N$-body simulations with CDM and FDM initial conditions. We go on to derive the respective lensing spectra, bispectra and trispectra in CDM and FDM in the context of a Euclid-like weak lensing survey. Finally, we compute the attainable cumulative signal-to-noise ratios and an estimate of the attainable $\chi^2$-functionals for distinguishing FDM from CDM at particle masses $m=10^{-21}$ eV, $m = 10^{-22}$ eV and $m = 10^{-23}$ eV. We find that PT predictions cannot be used to reliably distinguish the three models in a weak lensing survey. Assuming that $N$-body simulations overestimate the late-time small-scale power in the FDM model, future weak lensing survey might be used to distinguish between the FDM and CDM cases up to a mass of $m = 10^{-23}$ eV. However, observations probing the local high-$z$ universe are probably more suited to constrain the FDM mass.