CONFORMAL SPACE-TIMES - THE ARENAS OF PHYSICS AND COSMOLOGY

The mathematical and physical aspects of tire conformal symmetry of sp ace-time and of physical laws are analyzed. In particular, the group c lassification of conformally flat space-times, the conformal compactif ications of space-time, and the problem of imbedding of the flat space -time in global four-dimensional curved spaces with nontrivial topolog ical and geometrical structure are discussed in detail. The wave equat ions on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the implications of global compactified space-times for cosmology are discussed Ii is argu ed that the recent discovery of periodic structure of matter distribut ion on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spa tially compact Robertson-Walker space-time. II is shown that the energ y distribution in this model is periodic and the periods and density d ecrease with increasing distance, in striking agreement with experimen tal data. Our model of the universe also provides a definite predictio ns for the energy distribution, polar and azimuthal, considered as a f unction of angles theta and phi. These predictions should be tested wi th the new astronomical data.