Testing the scale-dependent hemispherical asymmetry with the 21-cm power
  spectrum from the epoch of reionization
  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 $k_{\rm
CMB}\simeq 0.0045\,{\rm Mpc}^{-1}$, 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 $0.056
\lesssim k_{\rm 21cm} \lesssim 0.15 \,{\rm Mpc}^{-1}$. 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.
