International Journal of Physics
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International Journal of Physics. 2016, 4(3), 64-68
DOI: 10.12691/ijp-4-3-4
Open AccessArticle

A 3D Brans-Dicke Theory Model

T. G. do Prado1, , E. F. Reis1, M. C. Vergės1, V. Piccirillo1 and J. R. Ciappina1

1Federal University of Technology-Paraná, Departament of Mathematics 84016-210, Ponta Grossa, PR, Brasil

Pub. Date: May 09, 2016

Cite this paper:
T. G. do Prado, E. F. Reis, M. C. Vergės, V. Piccirillo and J. R. Ciappina. A 3D Brans-Dicke Theory Model. International Journal of Physics. 2016; 4(3):64-68. doi: 10.12691/ijp-4-3-4


The evidence of an accelerated universe and the gap of 70 percent in the total energy, collected by WMAP, are problems that cannot be solved by standard models based on General relativity. Therefore the search for an alternative theory that solves the open questions in General Relativity became an important research field in the past few years. A particular alternative is the Brans-Dicke theory, which has been broadly studied as concerned to k-essence type fields in 4D. However, this theory is almost unexplored in the context of the dimensional reduction in 3D. In the present work, we study the Brans-Dicke Theory in a dimensional reduction context. In order to do this, we consider the Brans-Dicke theory in the vacuum, and in the presence of matter fields.

cosmology dimensional reduction general relativity lower dimensional gravitation

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[1]  E. Berti. Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity. Braz. J. Phys., 43:341-350, 2013.
[2]  J. C. Fabris, F. T. Falciano, J. Marto, N. Pinto-Neto, P. Vargas Moniz. Dilaton Quantum Cosmology with a Schrdinger-like Equation. Braz. J. Phys., 42:475-481, 2012.
[3]  D. N. Spergel et al. First year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters. Astrophys. J., 148:175, 2003. (arXiv:astro-ph/0302209).
[4]  P. Jordan. Schwerkraft undWeltall. Friedrich Vieweg und Sohn, Braunschweig, 1955.
[5]  Y. Fujii, K. Maeda. The scalar-tensor theory of gravitation. Cambridge University Press, Cambridge, 2004.
[6]  C. Brans, R. H. Dicke. Mach's principle and a relativistic theory of gravitation. Phys. Rev., 124:925, 1961.
[7]  R. H. Dicke. Mach's principle and invariance under transformation of units. Phys. Rev., 125:2163, 1962.
[8]  P. A. M. Dirac. New basis for cosmology. Proc. Roy. Soc., A165:199, 1938.
[9]  N. Banerjee, D. Pavon. A Quintessence scalar field in Brans-Dicke theory. Class. Quant. Grav., 18:593, 2001.
[10]  H. Kim. Brans-Dicke scalar field as a unique k-essence. Phys. Lett., B606:223, 2005.
[11]  L. Qiang, Y. Ma, M. Han, D. Yu. Five-dimensional Brans-Dicke theory and cosmic acceleration. Phys. Rev., D71:061501, 2005.
[12]  J. Ponce de Leon. Late time cosmic acceleration from vacuum Dicke theory in 5D. Class. Quantum Grav., 27:095002, 2010.
[13]  M. Ba~nados, C. Teitelboim, J. Zanelli. Black hole in three-dimensional spacetime. Phys. Rev. Lett., 69:1849, 1992.
[14]  O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, Y. Oz. Large N Field Theories, String Theory and Gravity. Phys. Reports, 323:183, 2000.
[15]  A. Maloney, W. Song, A. Strominger. Chiral gravity, log gravity and extremal CFT. Phys. Rev., D81:064007, 2010.
[16]  A. A. Bytsenko and M. E. X. Guimarães. Truncated heat kernel and one-loop determinants for the BTZ geometry. Eur. Phys. J. C., 58:511, 2008.
[17]  S. W. Hawking, G. F. R. Ellis. The large structure of space-time. Cambridge University Press, Cambridge, 1973.
[18]  E. Nabulsi, A. Rami. Effective cosmology a la Brans-Dicke with a non-minimally coupling massive inaton field interacting with minimally coupling massless field. Braz. J. Phys., 40(3):273, 2010.
[19]  D. A. Tretyakova, A. A. Shatskiy, I. D. Novikov, S. Alexeyev. Nonsingular Brans-Dicke ˄ cosmology. Phys. Rev., D85:124059, 2012.
[20]  S. V. Sushkov, S. M. Kozyrev. Composite vacuum Brans-Dicke wormholes. Phys. Rev., D84:124026, 2011.
[21]  K. H. Saaidi, A. Mohammadi, H. Sheikhahmadi. parameter and Solar System constraint in chameleon-Brans-Dicke theory. Phys. Rev., D83:104019, 2011.
[22]  Feng-Quan Wu and Xuelei Chen. Cosmic microwave background with Brans-Dicke gravity. II. Constraints with the WMAP and SDSS data. Phys. Rev., D82:083003, 2010.
[23]  Feng-QuanWu, Li-e Qiang, XinWang, Xuelei Chen. Cosmic microwave background with Brans-Dicke gravity. I. Covariant Formulation. Phys. Rev., D82:083002, 2010.
[24]  S. Weinberg. Gravitation and Cosmology. Wiley, Barbacena, 1972.
[25]  C. W. Misner, K. S. Thorne, J. A. Wheeler. Gravitation. W. H. Freeman and Company, 1973.