The gravitational scattering of the cosmic microwave background by dark clusters of galaxies

The spectrum distortion of the cosmic microwave background (CMB) due to the transverse peculiar motion of galaxy clusters was restudied. The fundamental equation for estimating the frequency shift of the photons that pass through the moving gravitational lensing object is derived from the geodesic equation. The fractional temperature fluctuation of the CMB induced by the transverse peculiar motion of a galaxy cluster was estimated to be a few times 10^-7. The effect is distinguishable from the CMB primary temperature fluctuation and other secondary effects by its peculiar dipole pattern in the cluster scale. The effect provides a new complemental method of confirming the existence of the dark cluster; otherwise, the gravitational lensing effect is the only reliable effect revealing the existence of such an exotic object.