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

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 $\Delta \simeq 225$ 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.