The distribution of matter fluctuations in our universe is key for understanding the nature of dark matter and the physics of the early cosmos .
Different observables have been able to map this distribution at large scales , corresponding to wavenumbers k \lesssim 10 Mpc ^ { -1 } , but smaller scales remain much less constrained .
In this work we study the sensitivity of upcoming measurements of the 21-cm line of neutral hydrogen to the small-scale matter power spectrum .
The 21-cm line is a promising tracer of early stellar formation , which took place in small haloes ( with masses M \sim 10 ^ { 6 } -10 ^ { 8 } M _ { \odot } ) , formed out of matter overdensities with wavenumbers as large as k \approx 100 Mpc ^ { -1 } .
Here we forecast how well both the 21-cm global signal , and its fluctuations , could probe the matter power spectrum during cosmic dawn ( z = 12 - 25 ) .
In both cases we find that the long-wavelength modes ( with k \lesssim 40 Mpc ^ { -1 } ) are highly degenerate with astrophysical parameters , whereas the modes with k = ( 40 - 80 ) Mpc ^ { -1 } are more readily observable .
This is further illustrated in terms of the principal components of the matter power spectrum , which peak at k \sim 50 Mpc ^ { -1 } both for a typical experiment measuring the 21-cm global signal and its fluctuations .
We find that , imposing broad priors on astrophysical parameters , a global-signal experiment can measure the amplitude of the matter power spectrum integrated over k = ( 40 - 80 ) Mpc ^ { -1 } with a precision of tens of percent .
A fluctuation experiment , on the other hand , can constrain the power spectrum to a similar accuracy over both the k = ( 40 - 60 ) Mpc ^ { -1 } and ( 60 - 80 ) Mpc ^ { -1 } ranges even without astrophysical priors .
The constraints outlined in this work would be able to test the behavior of dark matter at the smallest scales yet measured , for instance probing warm-dark matter masses up to m _ { WDM } = 8 keV for the global signal and 14 keV for the 21-cm fluctuations .
This could shed light on the nature of dark matter beyond the reach of other cosmic probes .