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 up
to fourth order to compute the tree-level matter trispectrum and the one-loop
matter spectrum and bispectrum from consistently chosen 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 a
weak lensing survey can potentially be used to distinguish between the FDM and
CDM cases up to a mass of $m={10}^{-22}$ eV.

PREPRINT

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

Alexander Kunkel, Tzihong Chiueh, Björn Malte Schäfer

Submitted on 2 November 2022

## Abstract

## Preprint

Comment: 18 pages, 25 figures

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics