Abstract
The gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such equality of all coordinate systems may not correspond to reality. Nevertheless, no actual verification of the necessity of this assumption has been made to date. The paper proposes a theory of gravity with a constraint, the degenerate variants of which are general relativity (GR) and the unimodular theory of gravity. This constraint is interpreted from a physical point of view as a sufficient condition for the adiabaticity of the process of the evolution of the space–time metric. The original equations of the theory of gravity with the constraint are formulated. On this basis, a unified model of the evolution of the modern, early, and very early Universe is constructed that is consistent with the observational astronomical data but does not require the hypotheses of the existence of dark energy, dark matter or inflatons. It is claimed that: physical time is anisotropic, the gravitational field is the main source of energy of the Universe, the maximum global energy density in the Universe was 64 orders of magnitude smaller the Planckian one, and the entropy density is 18 orders of magnitude higher the value predicted by GR. The value of the relative density of neutrinos at the present time and the maximum temperature of matter in the early Universe are calculated. The wave equation of the gravitational field is formulated, its solution is found, and the nonstationary wave function of the very early Universe is constructed. It is shown that the birth of the Universe was random.
Highlights
Over a hundred years ago, in the derivation of the gravitational equations from the variational principle, Hilbert formulated “an axiom of the general invariance of the action in relation to arbitrary transformations of the world parameters [coordinates]” and chose “R—the invariant built from the Riemann tensor [curvature of the four-dimensional manifold]” as the Lagrangian of the gravitational field [1].Three years earlier, Einstein wrote: “Besides, it should be emphasized that we have no basis whatever for assuming general covariance of the gravitational equations
The gravitational field is endowed with all the properties of a material medium: energy, pressure, entropy and temperature
By virtue of the definition of an energy–momentum density tensor adopted in the paper, the pressure of the gravitational field at the initial moment turns out to be negative, as a result of which the growth of the scale factor begins
Summary
Over a hundred years ago, in the derivation of the gravitational equations from the variational principle, Hilbert formulated “an axiom of the general invariance of the action in relation to arbitrary transformations of the world parameters [coordinates]” and chose “R—the invariant built from the Riemann tensor [curvature of the four-dimensional manifold]” as the Lagrangian of the gravitational field [1]. One possible way to construct a non-generally covariant theory of gravity without violating Hilbert’s axioms (as I see it) is the introduction of an a priori constraint that restricts the choice of coordinate system. The solution of the gravitational equations has enough free parameters to ensure the requirement of the equality of the inertial mass of the gravitational field to its gravitational mass, and to determine inertial mass in accordance with Mach’s principle (the latter problem has not been solved in GR) From this point of view, the results of experiments [9] should be considered as an indication that only such (quasi) stationary self-gravitating objects exist for which inertial mass is equal to gravitational mass. Due to the fact that GR is not a gauge theory [13], to avoid contradictions with the initial provisions, such a condition should be
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