The CMB temperature anisotropy, at each order (monopole, dipole, quadrupole etc) in the multipole expansion, is contributed by two effects: (i) partly by the motion of the earth w.r.t the CMB-the kinematic anisotropy and (ii) partly was (probably) caused by inflationary perturbations -the primordial anisotropy. Is it possible to distinguish and therefore, subtract the kinematic anisotropies from the net anisotropy to obtain the primordial anisotropies?
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$\begingroup$ Can you explain what you mean by, "at each order in the multipole expansion"? The Doppler shift anisotropy is always removed first, do you mean different kinematic anisotropies from the one caused by the Earth moving toward the Great Attractor? $\endgroup$– safesphereJul 2, 2018 at 20:14
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$\begingroup$ There are anisotropies due to the motion of earth w.r.t the CMB i.e., the effect of boost. I had asked a related question Finding the CMB temperature anisotropies contributed at different orders due to a uniform boost .I have just started to learn about CMB. $\endgroup$– SRSJul 2, 2018 at 20:16
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$\begingroup$ Got it, higher order spherical harmonics. I've been wondering as well of how the Doppler shift is subtracted. Thanks! (Also fixed what seemed to be a spelling error there. Hopefully this is what you meant. Otherwise please reject the edits.) $\endgroup$– safesphereJul 2, 2018 at 20:29
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The kinematic anisotropy is manifested solely in the dipole anisotropy; specifically, the $Y_{10}$ harmonic if the Earth's motion is taken along the z-axis.
