The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not co-moving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in Weyl FR, when it has hollow topological form in the space of Weyl FR and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this internal part of the space. Inevitability of self-organization in physical vacuum of spiral-wave structural elements, which correspond to elementary particles, and universal electromagnetic nature of all nonfictive particles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter.