The isotropy of CMB is one of the important tests of the modern cosmology. I am going to discuss the current and prospective tests of statistical anisotropy in the CMB:
(1) “Copi etal. (2009)” have been arguing that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, LCDM cosmology. I am going to argue that the “ad-hoc” discrepancy is due to the sub-optimal estimator of the low-l multipoles, and a posteriori statistics, which exaggerates the statistical significance. Therefore there is no actually lack of angular correlation in the CMB.
(2) I 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. I 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).
(3) LCDM model also predict the existence of primordial gravitational wave, for which B-mode polarization will be a powerful tool to distinguish different models of the early Universe.
In addition, I will discuss the Planck mission launched by European Space Agency in May/2012 to observe the CMB anisotropy, and its prospective scientific impact on precision cosmology.