By decomposing the CMB temperature fluctuations squared into spherical harmonics , we can define the 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 \sim 0.0015 , 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 .