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The EDGES experiment recently announced evidence for a broad absorptionfeature in the sky-averaged radio spectrum around 78 MHz, as may result fromabsorption in the 21 cm line by neutral hydrogen at z~15-20. If confirmed, oneimplication is that the spin temperature of the 21 cm line is coupled to thegas temperature by z=20. The known mechanism for accomplishing this is theWouthuysen-Field effect, whereby Lyman-alpha photons scatter in theintergalactic medium (IGM) and impact the hyperfine level populations. Thissuggests that early star formation had already produced a copious Lyman-alphabackground by z=20, and strongly constrains models in which the linear matterpower spectrum is suppressed on small-scales, since halo and star formation aredelayed in such scenarios. Here we consider the case that the dark matterconsists of ultra-light axions with macroscopic de Broglie wavelengths (fuzzydark matter, FDM). We assume that star formation tracks halo formation andadopt two simple models from the current literature for the halo mass functionin FDM. We further suppose that the fraction of halo baryons which form starsis less than a conservative upper limit of $f_\star \leq 0.05$, and that ~10^4Lyman-alpha to Lyman-limit photons are produced per stellar baryon. We findthat the requirement that the 21 cm spin temperature is coupled to the gastemperature by $z=20$ places a lower-limit on the FDM particle mass of $m_a\geq 5 \times 10^{-21} {\rm eV}$. The constraint is insensitive to the preciseminimum mass of halos where stars form. As the global 21 cm measurements arerefined, the coupling redshift could change and we quantify how the FDMconstraint would be modified. A rough translation of the FDM mass bound to athermal relic warm dark matter (WDM) mass bound is also provided.

The Implications of a Pre-reionization 21 cm Absorption Signal for Fuzzy Dark Matter