Testing a direction-dependent primordial power spectrum with
  observations of the Cosmic Microwave Background
  Statistical isotropy is often assumed in cosmology and should be tested
rigorously against observational data. We construct simple quadratic estimators
to reconstruct asymmetry in the primordial power spectrum from CMB temperature
and polarization data and verify their accuracy using simulations with
quadrupole power asymmetry. We show that the Planck mission, with its millions
of signal-dominated modes of the temperature anisotropy, should be able to
constrain the amplitude of any spherical multipole of a scale-invariant
quadrupole asymmetry at the $0.01$ level ($2\sigma$). Almost independent
constraints can be obtained from polarization at the $0.03$ level after four
full-sky surveys, providing an important consistency test. If the amplitude of
the asymmetry is large enough, constraining its scale-dependence should become
possible. In scale-free quadrupole models with $1\%$ asymmetry, consistent with
the current limits from WMAP temperature data (after correction for beam
asymmetries), Planck should constrain the spectral index $q$ of power-law
departures from asymmetry to $\Delta q = 0.3$. Finally, we show how to
constrain models with axisymmetry in the same framework. For scale-free
quadrupole models, Planck should constrain the direction of the asymmetry to a
$1\sigma$ accuracy of about $2$ degrees using one year of temperature data.
