PERTURBATIONS OF THE COSMIC MICROWAVE BACKGROUND-RADIATION AND STRUCTURE FORMATIONS

After the recent discovery of temperature fluctuations of the cosmic microwave background radiation by COBE, the study of the temperature fluctuations becomes more and more important for understanding formations of large scale structures of the universe. The treatments for the evolution of small density fluctuations of matters and radiation by gauge invariant formalism are summarized. And the expected values of temperature anisotropies in various cosmological models are shown. Both flat and open universe models with and without the cosmological constant are considered. As for open universe models, in particular, any work had never been done by the complete treatment on large scale anisotropies. However we could find the complete formula to handle large scale temperature anisotropies and here this formula is adopted. Using the results of COBE with previous measurements of temperature fluctuations which give the upper limits, severe and reliable constraints on various cosmological models are obtained. As a result, it is found that the desirable models are the dark matter dominated universe models with initially scale free power spectrum and the density parameter OMEGA0 congruent-to 1 while some models with low density are still allowed if the models have totally flat geometry by including the cosmological constant.