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# 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

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

Comment: 18 pages, 25 figures

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics