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A weak lensing perspective on nonlinear structure formation with fuzzy dark matter. (arXiv:2211.01523v3 [astro-ph.CO] UPDATED)

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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 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.

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