Brans-Dicke scalar field interactions in presence of radiation distribution

By considering the Robertson-Walker, line element exact solutions are obtained for radiation-filled cosmological differential equations of Brans-Dicke theory with the assumption thatk/k = 1/R, wherek denotes the gravitational variable andR is the radius of curvature and the dot denotes the differentiation with respect to time. Under this assumption, we obtain exact solutions corresponding to the three values of curvature indexK (1,0, –1). We can obtain physically realistic solutions in all the three cases for all values of coupling constant > –2. The radius of curvature increases linearly with respect to the age of the universe, while the gravitational variablek varies directly as the square of the radius of the universe. The solution obtained contradicts Dirac's hypothesis in which the gravitational constant should decrease with time in the expanding universe.