Abstract
The paper studies the modified theory of induced gravity (MTIG). The solutions of the MTIG equations contain two branches (stages): Einstein (ES) and “restructuring” (RS). Previously, solutions were found that the values of such parameters as the “Hubble parameter”, gravitational and cosmological “constants” at the RS stage, fluctuate near monotonously developing mean values. This article gives MTIG equations with arbitrary potential. Solutions of the equations of geodesic curves are investigated for the case of centrally symmetric space and quadratic potential at the RS stage. The oscillatory nature of the solutions leads to the appearance of a gravitational potential containing a spectrum of minima, as well as to antigravity, which is expressed by acceleration directed from the center. Such solutions lead to the distribution of the potential of the gravitational field creating an additional mass effect at large distances and are well suited for modeling the effect of dark matter in galaxies. The solutions of the equation of geodesic lines are obtained and analyzed. We found that the transition from flat asymptotics to oscillatory asymptotics at large distances from the center with a combination of the presence of antigravity zones leads to a rich variety of shapes and dynamics of geodesic curves and to the formation of complex structures.
Highlights
This work is a continuation of the author’s previous studies, which consider the modified theory of induced gravity (MTIG)
Such solutions lead to the distribution of the potential of the gravitational field creating an additional mass effect at large distances and are well suited for modeling the effect of dark matter in galaxies
We found that the transition from flat asymptotics to oscillatory asymptotics at large distances from the center with a combination of the presence of antigravity zones leads to a rich variety of shapes and dynamics of geodesic curves and to the formation of complex structures
Summary
This work is a continuation of the author’s previous studies, which consider the modified theory of induced gravity (MTIG). Despite the many experiments [2,3,4] to refine its value, the gravitational constant has not been determined even to the fourth decimal place This fact suggests the possible variations of the parameter G depending on the coordinates of space-time. We have shown that the quadratic potential of the scalar field and the inclusion of deviations of the metric from the Schwarzschild–De-Sitter metric up to the second order are essential factors for the realization of oscillatory solutions This fact can be compared with studies of nonlinear stability in the anti-de Sitter (AdS) space. The problem of breaking the conformal invariance of the theory arose, which was facilitated by the successful implementation of the principle of “spontaneous symmetry breaking” and the Higgs mechanism [30] for combining fundamental interactions Based on this approach, studying the action (8) at the transition point. The article [43] it is noted: “... negative kinetic energy in antigravity presents no problems of principles but is an interesting topic for physical investigations of fundamental significance”
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