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

The recent EDGES collaboration detection of the 21-cm 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. The small scale structure in the WDM model has a delayed formation time and therefore, requiring sufficiently strong Lyman-$\alpha$ background due to star formation at $z=18$, a stringent lower limit can be placed on $m_\chi$. Our results show that the coupling the spin temperature to the gas through Lyman-$\alpha$ pumping requires a minimum mass of $m_\chi>4$ keV if atomic cooling halos dominate the star formation rate at $z=18,$ and $m_\chi>3$ keV if $H_2$ cooling halos also form stars efficiently at this redshift. These lower 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.