Probing Fuzzy Dark Matter in the 21 cm Signal via Wavelet Scattering Transform

TL;DR

This work addresses whether fuzzy dark matter (FDM) can be distinguished from cold dark matter (CDM) using the redshifted 21 cm signal from Cosmic Dawn and the EoR. It applies the two-dimensional wavelet scattering transform (WST) to FDM-modified 21 cmFAST maps to extract high-order, multiscale, non-Gaussian features that encode wave-like suppression of small-scale structure and delayed heating/ionization. The authors demonstrate that first-order WST coefficients track scale-dependent variance while second-order coefficients capture cross-scale phase couplings, with robust separability between CDM and FDM even under SKA1-Low-like thermal noise; they quantify model separability with effect sizes and pairwise distances that peak for low-order scale pairs in $z\approx10$–$20$. The study shows that WST complements conventional power-spectrum analyses by revealing non-Gaussian morphology tied to the wave nature of dark matter, offering a promising, noise-tolerant diagnostic for forthcoming 21 cm observations.

Abstract

We explore the imprints of fuzzy dark matter (FDM) on the redshifted 21~cm signal from the Cosmic Dawn and the Epoch of Reionization by employing the wavelet scattering transform (WST). FDM, composed of ultralight scalar particles with masses $m_{\mathrm{FDM}} \sim 10^{-22}\,\mathrm{eV}$, exhibits quantum pressure that suppresses the formation of small-scale structures below the de~Broglie wavelength, thereby delaying star formation and modifying the thermal history of the intergalactic medium. Using modified \texttt{21cmFAST} simulations that incorporate both linear and nonlinear effects of FDM on structure formation, we analyze the two-dimensional 21~cm brightness temperature fields through the first- and second-order WST coefficients. The first-order coefficients, $S_1(j)$, quantify scale-dependent variance analogous to the power spectrum, while the normalized second-order ratio $R(j_1,j_2)=S_2/S_1$ captures non-Gaussian cross-scale couplings. We find that low-order couplings, particularly between large and intermediate scales, are highly sensitive to the FDM particle mass and remain robust under SKA1-Low-like thermal noise. Quantitatively, the WST coefficients yield pairwise distances of $Δ\simeq 225$ between CDM and FDM with $m_{\mathrm{FDM}}=10^{-22}\,\mathrm{eV}$, demonstrating that this framework can effectively discriminate between wave-like and cold dark matter scenarios even under realistic observational conditions. Our results establish the WST as a powerful, noise-tolerant statistical tool for probing the wave nature of dark matter through forthcoming 21~cm observations.

Figures (11)

• Figure 1: Global 21 cm brightness temperature $\delta T_b$ as a function of redshift for different dark matter scenarios. Top: Comparison between CDM and FDM models with masses $m=10\times 10^{-22}\,\mathrm{eV}$ and $m=50\times 10^{-22}\,\mathrm{eV}$, both with index parameter $\alpha=-1.1$. The timing and depth of the absorption trough vary significantly with mass, reflecting the suppression of small-scale power in lighter FDM. Bottom: Comparison between CDM and FDM with fixed mass $m=10\times 10^{-22}\,\mathrm{eV}$ but different indices, $\alpha=-0.8$ and $\alpha=-1.4$. In this case, both FDM curves deviate from CDM, but the difference between the two indices is relatively small.
• Figure 2: Dimensionless 21 cm power spectrum $\Delta^2_{21}(k,z)$ at representative wavenumbers $k=0.09$, $0.42$, and $1.0\,\mathrm{Mpc^{-1}}$ as a function of redshift. Top: Comparison between CDM and FDM models with masses $m=10\times10^{-22}\,\mathrm{eV}$ and $m=50\times10^{-22}\,\mathrm{eV}$, both with $\alpha=-1.1$. The suppression of small-scale structure in light FDM shifts and weakens the Ly$\alpha$-coupling, heating, and reionization peaks. Bottom: Comparison between CDM and FDM with fixed mass $m=10\times10^{-22}\,\mathrm{eV}$ but different indices, $\alpha=-0.8$ and $\alpha=-1.4$. The index parameter primarily affects the amplitude of the heating peak, while the overall timing is governed by the FDM mass. All panels share the same color scale and axis limits for direct comparison.
• Figure 3: First-order WST coefficients without thermal noise. Top: Dependence on the dark matter particle mass ($\alpha=-1.1$). Bottom: Dependence on the $\alpha$ index in the FDM HMF ($m=10$). The redshift evolution of $S_1(j)$ parallels the global and power-spectrum trends: lighter FDM models shift the peak to lower redshift and suppress small-scale fluctuation power, while variations in $\alpha$ produce only minor amplitude modulations. All panels share the same color scale and axis limits for direct comparison.
• Figure 4: Second–order wavelet–scattering ratio $R=S_2/S_1$ without thermal noise. Top: Dependence on the dark–matter particle mass. Bottom: Dependence on the $\alpha$ index in the FDM HMF at fixed mass.
• Figure 5: Effect of instrumental response and thermal noise on simulated 21-cm images. Left: Clean signal without instrumental effects. Middle: Interferometrically filtered image showing spatial smoothing due to limited uv coverage. Right: Mock observation including both finite resolution and thermal noise; small-scale random fluctuations dominate while large-scale structures remain visible.