Constraints on freeze-in dark matter from Lyman-$\alpha$ forest and 21-cm signal : single-field models

We report new Lyman-$\alpha$ and 21-cm constraints on freeze-in dark matter (FIDM) which injects energy into the intergalactic medium either through annihilation or decay to photon(s) or electron-positron pair. With respect to Lyman-$\alpha$ we fix the baseline ionization history using low redshift data about astrophysical reionization, whereas for 21-cm signal we adopt the baseline values of 21-cm power spectrum through a standard modeling of star formation developed so far. Using the latest numerical tools, we show that (i) for sterile neutrino FIDM, current Lyman-$\alpha$ data and future sensitivity of SKA-low (1000 hrs) on the 21-cm power spectra excludes the FIDM mass up to $1.8\times {10}^{-3}$ GeV at 95$\mathrm{\%}$ CL and $5.46\times {10}^{-4}$ GeV, respectively, and (ii) for millicharged FIDM, current Lyman-$\alpha$ data only excludes the millicharge down to ${10}^{-8}$ within the FIDM mass range of ${10}^{-3}-1$ GeV at 95$\mathrm{\%}$ CL, suggesting that the surviving parameter space of millicharged FIDM is still intact.