The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological `Coupling Constants’ in the Theory of Induced Gravity

Abstract

This work is the extension of author's research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and "restructuring" (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological "constants" , which are defined by the "mean square" of the scalar fields. In obtained solutions the values of such parameters as "Hubble parameter", gravitational and cosmological "constants" in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton's law of gravitational interaction, antigravity. Telescope (HST) and Planck observatory [5]. The Hubble Space Telescope is tuned to measure the parallax Milky Way Cepheid variables and the distances are 1.7-3.6 kpc (the modern Universe). The measurements of the Planck spacecraft correspond to distant galaxies (the early Universe is about 375,000 years old). In 2018, the accuracy of the measurement of H 0 is increased to 2.3 percent, which gives H 0 = 73.48 ± 1.66 km · s −1 Mpc −1 . In the early Universe, based on the data received from the "Planck" spacecraft and ΛCDM theory, the predicted value is H 0 = 67.0 ± 1.2 km · s −1 Mpc −1 . The difference is about 9 percent. The accuracy of the measurements is about 4.5 percent. There is also a variance in the observations made at different times and different methods. For example, as indicated in the work [6], the local and direct definition of H 0 gives H 0 = 73.24 ± 1.74 km · s −1 Mpc −1 , and the most recent value from [7] in consent with ΛCDM is 66.93 ± 0.62 km · s −1 Mpc −1 . In our opinion, the problem can be reduced to a strong binding of calculations of the Hubble parameter H 0 to the ΛCDM model. In our work we present a model where, due to the oscillatory regime in the solutions of equations, the Hubble parameter also fluctuates with respect to the mean value-which is also a function of time.3. The problems of so-called "dark energy" (DE) and "dark matter" (DM). The first of them can be reduced to the problem of existence and smallness of the "cosmological constant" (par. 1). The challenge posed by the cosmological constant problem [1] has spurred many attempts at directly modifying Einstein's gravity at large distances [8]. As example of s...

Dark Matter as a Result of Field Oscillations in the Modified Theory of Induced Gravity

“…In the article [8], we proposed, as a discussion, that for the later evolutionary time, the oscillation amplitudes of the Hubble constant should increase compared to previous times. From a numerical comparison with our various [8] models, it follows that this paradox is better explained by the so-called "stochastic models" (Purusha Universe in [7].…”

“…In works [7,8], we presented a model in which, due to the oscillatory regime in the solutions of equations, the Hubble parameter also oscillates relative to the average value. In the article [8], we proposed, as a discussion, that for the later evolutionary time, the oscillation amplitudes of the Hubble constant should increase compared to previous times.…”

“…In order to try to solve the above problems and compare them with observations of DE and DM, a phenomenological model of the modified theory of induced gravity (MTIG) was proposed, which is described in our works [7,8,[13][14][15]. In a simplified version of the theory, we made an attempt to introduce a certain macroscopic parameter of the theory Y, which generates both gravitational (G e f f ) and cosmological (Λ e f f ) "constants" [7]:…”

“…where U e f f = U e f f (Y)-effective potential of the theory (note: the definition of U e f f in this article differs from its definition in articles [7,8]); G e f f some function of Y depending on the type of potential U e f f (Y).…”

“…In our works [7], we compare the Newtonian gravitational constant (k n ) with the effective "gravitational constant".…”