A limit on the warm dark matter particle mass from the redshifted 21 cm absorption line

The recent EDGES collaboration detection of an absorption signal at a central frequency of $\nu = 78 \pm 1$ MHz points to the presence of a significant Lyman-$\alpha$ background by a redshift of $z=18$. The timing of this signal constrains the dark matter particle mass ($m_\chi$) in the warm dark matter (WDM) cosmological model. WDM delays the formation of small-scale structures, and therefore a stringent lower limit can be placed on $m_\chi,$ based on the presence of a sufficiently strong Ly-$\alpha$ background due to star formation at $z=18$. Our results show that the coupling the spin temperature to the gas through Ly-$\alpha$ pumping requires a minimum mass of $m_\chi>3$ keV if atomic cooling halos dominate the star formation rate at $z=18,$ and $m_\chi>2$ keV if ${\rm\,H_2}$ cooling halos also form stars efficiently at this redshift. These limits match or exceed the most stringent limits cited to date in the literature, even in the face of the many uncertainties regarding star-formation at high redshift.