Detecting CMB modulations and non-Gaussianities from power multipoles
  By decomposing the CMB temperature fluctuations \emph{squared} into spherical
harmonics, we can define the \emph{CMB power multipoles} as the fundamental
observables to quantify any generic modulations in the CMB. This allows for
simple direct measurements for the CMB modulations, and also indirect
measurements for the CMB trispectrum, which fully determines the CMB
modulations in a statistically isotropic universe. The CMB power multipoles can
reach the theoretical accuracies higher than the current constraints from
Planck observations. The theoretical accuracy for the dipole modulation,
$A\sim0.0015$, receives $\sim 10$ times improvement; higher $l$ modulations
have even higher accuracies. This calls for practical observational studies of
its possible improvements on the CMB modulation and non-Gaussianity
constraints.
