Exact solution to radiation-filled Brans-Dicke closed space cosmology
Under the assumption of a power law (k·Rn=C,C=const.) between the gravitational constantk and the radius of curvatureR of the Universe and forP=1/3σ the exact solution is sought for the cosmological equations of Brans and Dicke. The solution turns out to be valid for closed space and the parameter ω of the scalar-tensor theory is necessarily negative. The radius of curvature increases linearly with respect to the age of the Universe while the gravitational constant grows with the square of the radius of curvature. It has been shown (Lessner, 1974) that in this case (K∼R2) the spatial component of the field equations is independent of the remaining equations. However, our solution satisfies this independent equation. This solution for the radiation-dominated era corresponds to the solution for the matter-dominated era found by Dehnen and one of the authors (Dehnen and Obregón, 1971). Our solution, as is the solution previously obtained for the matter-dominated era, is in contradiction to Dirac's hypothesis in which the gravitational constant should decrease with time in an expanding Universe.
KeywordsExact Solution Field Equation Gravitational Constant Spatial Component Closed Space
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- Brans, C. and Dicke, R. H.: 1961,Phys. Rev. 124, 925.Google Scholar
- Dehnen, H. and Obregón, O.: 1971,Astrophys. Space Sci. 14, 454.Google Scholar
- Dehnen, H. and Obregón, O.: 1972a,Astrophys. Space Sci. 15, 326.Google Scholar
- Dehnen, H. and Obregón, O.: 1972b,Astrophys. Space Sci. 17, 338.Google Scholar
- Dirac, P. A. M.: 1937,Nature 139, 323.Google Scholar
- Dirac, P. A. M.: 1938,Proc. Roy. Soc. (London) A165, 199.Google Scholar
- Lessner, G.: 1974,Astrophys. Space Sci. 30, L5.Google Scholar
- Morganstern, R. E.: 1971,Phys. Rev. D4, 282.Google Scholar
- Obregón, O. and Pimentel, O.: 1978, to appear inGen. Rel. Grav. Google Scholar
- O'Hanlon, J. and Tupper, B. O. J.: 1972,Nuovo Cimento 7b, 305.Google Scholar
- Schäfer, G. and Dehnen, H.: 1976,Astron. Astrophys. 54, 823.Google Scholar