Exact solution to radiation-filled Brans-Dicke closed space cosmology

Abstract

Under the assumption of a power law (k·R n=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∼R 2) 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 Obregon, 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.