GRAVITATIONAL OPTICAL SCINTILLATION AND ANISOTROPY OF THE COSMIC MICROWAVE BACKGROUND

We propose that the stochastic component of matter distribution in the universe may cause the apparent intensity fluctuation of radiation sources at cosmological distance. This phenomenon is in fact due to the gravitational lensing effect of random matter distribution and is referred to as gravitational optical scintillation. Using Maxwell equation in a linearly perturbed universe, we formulate this effect in terms of a scattering process by the gravitational potential. The anisotropy correlation function of light intensity fluctuation is obtained. It is then applied to study the temperature pattern of cosmic background radiation. We find that the gravitational optical scintillation gives a significant contribution to the anisotropy of CBR temperature fluctuation after the decoupling era and dominates on a scale of arc minutes. Numerical results are presented based on a variety of galaxy formation models. The rersults show that hot dark matter, adiabatic or isocurvature cold dark matter, and baryonic models with OMEGA = 1 are incompatible with the upper limit of CBR anisotropy given by recent observations. The anisotropy of CBR temperature fluctuation due to gravitational optical scintillation places a stringent constraint on galaxy formation models and serves as an indicator of the matter distribution in universe. As a result, we conclude that in the flat Einstein-de Sitter universe predicted strongly by the inflationary scenario, the luminous and underlying dark matter might have different distributions, namely, the luminous objects are inhomogeneous as observed today, while the dark matter has a smooth density distribution.