Violation of statistical isotropy and homogeneity in the 21-cm power
  spectrum
  Most inflationary models predict primordial perturbations to be statistically
isotropic and homogeneous. Cosmic microwave background (CMB) observations,
however, indicate a possible departure from statistical isotropy in the form of
a dipolar power modulation at large angular scales. Alternative models of
inflation, beyond the simplest single-field slow-roll models, can generate a
small power asymmetry, consistent with these observations. Observations of
clustering of quasars show, however, agreement with statistical isotropy at
much smaller angular scales. Here, we propose to use off-diagonal components of
the angular power spectrum of the 21-cm fluctuations during the dark ages to
test this power asymmetry. We forecast results for the planned SKA radio array,
a future radio array, and the cosmic-variance-limited case as a theoretical
proof of principle. Our results show that the 21-cm line power spectrum will
enable access to information at very small scales and at different redshift
slices, thus improving upon the current CMB constraints by $\sim 2$ orders of
magnitude for a dipolar asymmetry and by $\sim 1-3$ orders of magnitude for a
quadrupolar asymmetry case.
