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) and in its improved version — the relativistic gravithermodynamics (RGTD) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not comoving 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 the comoving with expanding Universe FR (CFREU), when it has hollow topological form in the space of CFEU 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 quasiparticles, and universal electromagnetic nature of all non-fictive quasiparticles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter. It is proved that only in the case of the joint application in the Universe of a physically homogeneous exponential scale of unified gravithermodynamic time and a dynamic gravitational field, which ensure the invariance in space and time of the vacuum velocity of light and the Hubble constant, is it possible to ensure not only the general covariance of all physical laws, but also the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter. Although the use in the Universe of a metrically homogeneous uniform scale of the proper time of matter and of a static gravitational field ensure the eternity of the existence of the Universe and the non-exceeding of the values of the false coordinate velocities of light of the GR by the radial velocities of distant galaxies, it does not ensure both the general covariance of all physical laws and the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter.