The EDGES experiment recently announced evidence for a broad absorption feature in the sky-averaged radio spectrum around 78 \mbox { MHz } , as may result from absorption in the 21 cm line by neutral hydrogen at z \sim 15 - 20 .
If confirmed , one implication is that the spin temperature of the 21 cm line is coupled to the gas temperature by z = 20 .
The known mechanism for accomplishing this is the Wouthuysen-Field effect , whereby Lyman-alpha photons scatter in the intergalactic medium ( IGM ) and impact the hyperfine level populations .
This suggests that early star formation had already produced a copious Lyman-alpha background by z = 20 , and strongly constrains models in which the linear matter power spectrum is suppressed on small-scales , since halo and star formation are delayed in such scenarios .
Here we consider the case that the dark matter consists of ultra-light axions with macroscopic de Broglie wavelengths ( fuzzy dark matter , FDM ) .
We assume that star formation tracks halo formation and adopt two simple models from the current literature for the halo mass function in FDM .
We further suppose that the fraction of halo baryons which form stars is less than a conservative upper limit of f _ { \star } \leq 0.05 , and that \sim 10 ^ { 4 } Lyman-alpha to Lyman-limit photons are produced per stellar baryon .
We find that the requirement that the 21 cm spin temperature is coupled to the gas temperature by z = 20 places a lower-limit on the FDM particle mass of m _ { a } \geq 5 \times 10 ^ { -21 } { eV } .
The constraint is insensitive to the precise minimum mass of halos where stars form .
As the global 21 cm measurements are refined , the coupling redshift could change and we quantify how the FDM constraint would be modified .
A rough translation of the FDM mass bound to a thermal relic warm dark matter ( WDM ) mass bound is also provided .