CMB Multipole Expansion in a Frame Dragging-Sustained Milky Way

We study the impact on the cosmic microwave background (CMB) landscape of peculiar rotational general relativistic effects. These effects, on galactic scales, do not possess a Newtonian analogue, and therefore could a priori impact CMB analysis. We find that the velocity inferred from the CMB dipole, under the kinematic interpretation, coincides with that measured by a stationary observer within the Milky Way and not with the one measured by the zero angular momentum observer. We show that the galaxy peculiar frame-dragging effects do not impact the standard CMB analysis, as these modify the multipole coefficients only at higher orders with respect to the dominant terms. Moreover, we prove that no general relativistic framework at the galactic scale patched within the standard cosmological model can account for the current tension on the CMB quadrupole amplitude.