The original Brans-Dicke scalar-tensor gravity is believed to be attracted towards General Relativity with evolution of the Universe. In the presence of explicit scalar-matter direct coupling in the Brans-Dicke gravity, however, the attractor mechanism must be reconsidered. In this paper, the master equation found by Damour and Nordtvedt is rederived. It is shown that such a generalized master equation could modify the attraction to General Relativity and the scalar-matter direct coupling may accelerate or retard it. In original Brans-Dicke scalar-tensor gravity, the agent of the attraction to General Relativity is the gravitational coupling strength. However, in the presence of the scalar-matter direct coupling, the coupling function which characterizes the coupling of scalar field to matter, makes another potential associated with coupling and it produces a new coupling parameter in the existence of the scalar-matter direct coupling, the master equation which describes the evolution of scalar field, comes to have the force term of right hand side an additional term characterizing the scalar-matter coupling, i.e. the coupling parameter is lying in parallel with the strength parameter. Therefore, the attraction mechanism represented by the strength parameter alone comes to be modified by adding the new coupling parameter. The paper considered, in detail, the friction-dominated approximation which is a case of a negligible curvature of the scalar-curvature coupling potential. Then, depending on the sign of a new coupling parameter, the evolution of scalar field is shown to accelerate the attraction or to retard it. Consequently, the attraction towards General Relativity is modified on account of the scalar-matter direct coupling.
| Published in | American Journal of Modern Physics (Volume 15, Issue 2) |
| DOI | 10.11648/j.ajmp.20261502.13 |
| Page(s) | 30-35 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2026. Published by Science Publishing Group |
Brans-Dicke Gravity, General Relativity, Cosmology
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APA Style
Kim, J. S., Ri, S. C., Kim, I. G., Kim, R. G. (2026). The Scalar-matter Direct Coupling and Attraction of Brans-Dicke Gravity to General Relativity. American Journal of Modern Physics, 15(2), 30-35. https://doi.org/10.11648/j.ajmp.20261502.13
ACS Style
Kim, J. S.; Ri, S. C.; Kim, I. G.; Kim, R. G. The Scalar-matter Direct Coupling and Attraction of Brans-Dicke Gravity to General Relativity. Am. J. Mod. Phys. 2026, 15(2), 30-35. doi: 10.11648/j.ajmp.20261502.13
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Download@article{10.11648/j.ajmp.20261502.13,
author = {Jik Su Kim and Song Chol Ri and Il Guk Kim and Ryong Gwang Kim},
title = {The Scalar-matter Direct Coupling and Attraction of
Brans-Dicke Gravity to General Relativity},
journal = {American Journal of Modern Physics},
volume = {15},
number = {2},
pages = {30-35},
doi = {10.11648/j.ajmp.20261502.13},
url = {https://doi.org/10.11648/j.ajmp.20261502.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20261502.13},
abstract = {The original Brans-Dicke scalar-tensor gravity is believed to be attracted towards General Relativity with evolution of the Universe. In the presence of explicit scalar-matter direct coupling in the Brans-Dicke gravity, however, the attractor mechanism must be reconsidered. In this paper, the master equation found by Damour and Nordtvedt is rederived. It is shown that such a generalized master equation could modify the attraction to General Relativity and the scalar-matter direct coupling may accelerate or retard it. In original Brans-Dicke scalar-tensor gravity, the agent of the attraction to General Relativity is the gravitational coupling strength. However, in the presence of the scalar-matter direct coupling, the coupling function which characterizes the coupling of scalar field to matter, makes another potential associated with coupling and it produces a new coupling parameter in the existence of the scalar-matter direct coupling, the master equation which describes the evolution of scalar field, comes to have the force term of right hand side an additional term characterizing the scalar-matter coupling, i.e. the coupling parameter is lying in parallel with the strength parameter. Therefore, the attraction mechanism represented by the strength parameter alone comes to be modified by adding the new coupling parameter. The paper considered, in detail, the friction-dominated approximation which is a case of a negligible curvature of the scalar-curvature coupling potential. Then, depending on the sign of a new coupling parameter, the evolution of scalar field is shown to accelerate the attraction or to retard it. Consequently, the attraction towards General Relativity is modified on account of the scalar-matter direct coupling.},
year = {2026}
}
TY - JOUR T1 - The Scalar-matter Direct Coupling and Attraction of Brans-Dicke Gravity to General Relativity AU - Jik Su Kim AU - Song Chol Ri AU - Il Guk Kim AU - Ryong Gwang Kim Y1 - 2026/03/16 PY - 2026 N1 - https://doi.org/10.11648/j.ajmp.20261502.13 DO - 10.11648/j.ajmp.20261502.13 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 30 EP - 35 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20261502.13 AB - The original Brans-Dicke scalar-tensor gravity is believed to be attracted towards General Relativity with evolution of the Universe. In the presence of explicit scalar-matter direct coupling in the Brans-Dicke gravity, however, the attractor mechanism must be reconsidered. In this paper, the master equation found by Damour and Nordtvedt is rederived. It is shown that such a generalized master equation could modify the attraction to General Relativity and the scalar-matter direct coupling may accelerate or retard it. In original Brans-Dicke scalar-tensor gravity, the agent of the attraction to General Relativity is the gravitational coupling strength. However, in the presence of the scalar-matter direct coupling, the coupling function which characterizes the coupling of scalar field to matter, makes another potential associated with coupling and it produces a new coupling parameter in the existence of the scalar-matter direct coupling, the master equation which describes the evolution of scalar field, comes to have the force term of right hand side an additional term characterizing the scalar-matter coupling, i.e. the coupling parameter is lying in parallel with the strength parameter. Therefore, the attraction mechanism represented by the strength parameter alone comes to be modified by adding the new coupling parameter. The paper considered, in detail, the friction-dominated approximation which is a case of a negligible curvature of the scalar-curvature coupling potential. Then, depending on the sign of a new coupling parameter, the evolution of scalar field is shown to accelerate the attraction or to retard it. Consequently, the attraction towards General Relativity is modified on account of the scalar-matter direct coupling. VL - 15 IS - 2 ER -
Pyongyang Astronomical Observatory, Pyongyang, Democratic People’s Republic of Korea
Department of Physics, Sariwon Ri Kye Sun University of Education, Sariwon, Democratic People’s Republic of Korea
Pyongyang Astronomical Observatory, Pyongyang, Democratic People’s Republic of Korea
Pyongyang Astronomical Observatory, Pyongyang, Democratic People’s Republic of Korea
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