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

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 χ2-functionals for distinguishing FDM from CDM at particle masses m=1021 eV, m=1022 eV and m=1023 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=1022 eV.

Preprint

Comment: 18 pages, 25 figures

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics

URL: http://arxiv.org/abs/2211.01523

Asymptotic behaviour of growing modes represented via the quotient of FDM and CDM growth factors $D_{+,FDM}(k, a)/D_{+, CDM}(a)$ in a FDM-dominated EdS universe for $m = 10^{-23}$ eV. The graphs show the analytical, divergent expression $\eqref{eq:FDMLinearGrowthASolution}$, the renormalised expression using the fifth-order Taylor expansion, the numerical solution obtained by integrating the linear growth equation with initial conditions given by Eq. \eqref{eq:CorrectIC} as well as a mean growth model $D(k, a) \approx \Bigl(1 + \alpha \left(\frac{k}{k_J}\right)^{\beta}\Bigl) D_{\mathrm{CDM}}(a)$ with the fit parameters $\alpha = 0.17$, $\beta = 6.50$ obtained via fitting to the analytical solution.