Gravitational angular fluctuations of the cosmic background radiation produced by cosmological linear perturbations

The gravitational angular fluctuations of light rays produced by linear density perturbations are investigated in the Einstein-de Sitter model. It is shown that, owing to the random-walk process aroused by the perturbations, the mean square of relative angular fluctuations of two neighbouring light rays increase as they propagate. If the density contrast is larger than 3 x 10-3 for the present size 30 Mpc, the angular fluctuations for the angle difference of several minutes are so large to play a role to decrease the small-scale anisotropy of the cosmic background radiation during the propagation from the decoupling epoch to the present. They may give us also a reason to the question why few quasars can be found for z > 4. (author)