I have been devoting myself to solving the problems of the theory of relativity and cosmology for more than 30 years. I've received many interesting results. And I want to make these results available for all scientists. Evolutionary self-contraction of microobjects of lower layers of gravithermodynamically bonded matter outpaces the similar self-contraction of its upper layers. This is the exact reason of the curvature of intrinsic space of matter. That is why gravitational field itself should be primarily considered as the field of spatial inhomogeneity of evolutionary decreasing of the size of matter microobjects in the background Euclidean space of expanding Universe. In correspondence to this the gravitational field itself is the field of spatial inhomogeneity of gravithermodynamic state of dense matter of compact astronomical objects, as well as of strongly rarefied gas-dust matter of space vacuum. And, therefore, the gravitational field fundamentally cannot exist without matter. That is why it is not an independent form of matter. It is shown that equations of the gravitational field of General Relativity (GR) should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR. The equivalence of only inert free energy of matter (and not of the total internal energy) to gravitational and inert masses is justified. It was proved that total energy of matter of inertially moving body is equal in all frames of references of spatial coordinates and time that are moving relatively to matter. And that is precisely why there is a conform Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity (SR). Conformal relativistic transformations of increments of metrical spatial segments and metrical temporal intervals (instead of increments of coordinates and coordinate time of SR) were received. It is also shown that the tensor of energy-momentum of matter (right side of the gravitational field equation) should be formed not being based on external thermodynamic parameters, but being based exactly on the intranuclear gravithermodynamic parameters. In this case the observed motion of astronomical objects of the galaxies is provided at arbitrary small density of mass of the matter on their periphery and, consequently, the presence of dark non-baryonic matter in the Universe is unnecessary. Of course, bodies free fall in gravitational field is an original realization of their tendency to increase the evolutionary self-contraction of microobjects of their matter, and the realization of the tendency of the whole gravitationally bonded inhomogeneous matter to the minimum of the integral values of its inert free energy and thermodynamic Gibbs free energy. Bodies that fall accelerate independently in spatially inhomogeneous medium of the outer space or atmosphere. Such bodies transform their continuously released intra-atomic energy into kinetic energy.

It is shown that in case of bodies’ free fall the gravitational deceleration of the rate of their intrinsic time is completely compensated by the motion due to isotropic all-round conformal gauge self-contraction of the size of falling bodies in the background Euclidean space of the Universe. Clocks that fall free are inertially moving and, therefore, continue to count time at the same rate as when they were in the state of rest. Similarly, the rate of time of astronomical body is not changed in the process of its motion in elliptical orbit. The dilatation of intrinsic time of distant galaxies is also absent, which points on the fact that Etherington identity does not correspond to reality. The fact that Hubble’s redshift is linearly dependent on transversal comoving distance instead of uncorrected luminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. According to this the presence of dark energy in the Universe is also unnecessary. For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of several wave functions that can take arbitrary values with certain probability. Being based on the united electromagnetic nature of all matter microobjects, I have proposed the spiral-wave models of all non-fictive elementary particles (positron, electron, muon and also quarks, which are confined by the singular surface, and other particles and antiparticles that consist of quarks). I've found out the alternatives to the Big Bang of Universe and to the black holes. It was shown that singular Schwarzschild sphere belongs only to infinitely far cosmological future and that its radius in background Euclidean space is equal to zero. And, consequently, the collapse of matter under the Schwarzschild sphere is fundamentally impossible. It was shown that the tendency of improper value of velocity of light to zero can correspond to the tendency of pressure and temperature in matter only to infinity. And, consequently, non-fictive singular surface can be only median. And in arbitrary massive astronomical objects, which have the topology of hollow body and mirror symmetry of intrinsic space, the singular surface separates the external matter from antimatter and as, a result, prevents their catastrophic annihilation. I've shown, that annihilation of matter and antimatter is the source of the quasars' energy and that gravitational waves are the phase waves (which don't transport energy) of the change of collective space-time state of matter and physical vacuum. And that's why these waves can propagate at supraluminal velocity.

Curved intrinsic space of the hollow astronomical body