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We investigate nonlinear structure formation in the fuzzy dark matter (FDM)model in comparison to cold dark matter (CDM) models from a weak lensingperspective using perturbative methods. We use Eulerian perturbation theory(PT) up to fourth order to compute the tree-level matter trispectrum and theone-loop matter spectrum and bispectrum from consistently chosen initialconditions. In addition, we predict the non-linear matter power spectra using$N$-body simulations with CDM and FDM initial conditions. We go on to derivethe respective lensing spectra, bispectra and trispectra in CDM and FDM in thecontext of a Euclid-like weak lensing survey. Finally, we compute theattainable 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 PTpredictions cannot be used to reliably distinguish the three models in a weaklensing survey. Assuming that $N$-body simulations overestimate the late-timesmall-scale power in the FDM model, future weak lensing survey might be used todistinguish 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 moresuited to constrain the FDM mass.

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