On the anisotropies of cosmic microwave background radiation

The work gives a brief overview of the topic of cosmic microwave background radiation anisotropies. Then is deals with the so-called Rees-Sciama affect; i.e. with the anisotropies arising between the last scattering surface and us due to transparent huge irregularities. Using the formulas of Special Theory of Relativity it is proven that in the neighbourhood of expanding spherical body the Meszaros calculation (Meszaros 1994) are correct; the inaccuracy is maximally of order 10-12. Then the profile of the blue shift of expansion caused by an expanding sphere is calculated for the case, when the radius of this sphere is much smaller that the relevant Hubble radius. Hence the profiles of the shifts of light periods through a void and through a supercluster are given in the most general cases. These cases contain all the three Friedmannian models and both the synchronous and asynchronous clusters. Then the obtained profiles are explicitly decomposed into the sum of the multipole terms, and it is shown that the observed difference between the measured direction of the maximum of dipole anisotropy of cosmic microwave background radiation and the result of Lauer and Postman (1994) is not explainable by the Rees-Sciama effect. This means that no alternative exists to the two possibilities for the explanation of the data of Lauer and Postman; either the either the huge system of Abell clusters is streaming, or the Friedmannian model is queried. The third possibility is, of course, that the data of observations of Lauer and Postman are incorrect. However, any of these three possibilities seem to be strange enough; hence, the problems coming from data of Lauer and Postman further holds. This is the key result of paper. As a further technical result it is also shown that in principle there is no upper limit of Rees-Sciama effect. (author)