Minimal anisotropy of the microwave background radiation in the gravitational instability picture

It is pointed out that the microwave background radiation photons carry information about the environment, and state of motion, of the material which has scattered them. They provide, therefore, an important test of theories of galaxy formation since different theories predict widely differing residual radiation anisotropy. The present investigation is concerned with the residual anisotropy arising if the universe were optically thick to electron scattering at some time after the standard epoch of recombination. The residual anisotropy can be ascribed to the peculiar motion of the last scatterers. The main result of the investigation is an equation which provides a fairly exact relation between the residual anisotropy of the radiation and the density perturbations existing at the epoch of last scattering, under the assumption that the universe became transparent at z less than 1000.