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The theoretical basis for the prediction of anisotropies in the cosmic microwave background is very well developed. Very low amplitude density and temperature perturbations produce small gravitational effects, leading to an anisotropy that is a combination of temperature fluctuations at the surface of last scattering and gravitational redshifts both at last scattering and along the path to the observer. All of the primary anisotropy can be handled by linear perturbation theory, which allows a very accurate calculation of the predicted anisotropy from different models of the Universe.
E. L. Wright (Thu,) studied this question.