Hemispherical power asymmetry has emerged as a new challenge to cosmology in early universe .
While the cosmic microwave background ( CMB ) measurements indicated the asymmetry amplitude A \simeq 0.07 at the CMB scale k _ { CMB } \simeq 0.0045 { Mpc } ^ { -1 } , the high-redshift quasar observations found no significant deviation from statistical isotropy .
This conflict can be reconciled in some scale-dependent asymmetry models .
We put forward a new parameterization of scale-dependent asymmetric power spectrum , inspired by a multi-speed inflation model .
The 21-cm power spectrum from the epoch of reionization can be used to constrain the scale-dependent hemispherical asymmetry .
We demonstrate that an optimum , multi-frequency observation by the Square Kilometre Array ( SKA ) Phase 2 can impose a constraint on the amplitude of the power asymmetry anomaly at the level of \Delta A \simeq 0.2 at 0.056 \lesssim k _ { 21 cm } \lesssim 0.15 { Mpc } ^ { -1 } .
This limit may be further improved by an order of magnitude as \Delta A \simeq 0.01 with a cosmic variance limited experiment such as the Omniscope .