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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.