Machian Cosmological Solution in the Generalized Scalar-Tensor Theory of Gravitation

Abstract

The Machian cosmological solution satisfying $\varphi =O(\rho /\omega )$ is discussed for the homogeneous and isotropic universe with a perfect fluid (with negative pressure) in the generalized scalar-tensor theory of gravitation. We propose $\omega (\varphi )=\eta /(\xi -2)$ for the coupling function in the Machian point of view. The parameter $\xi$ varies in time very slowly from $\xi =0$ to $\xi =2$ because of the physical evolution of matter in the universe. When $\xi \to 2$, the coupling function diverges to $-\infty$ and the scalar field $\varphi$ converges to $G_{\infty }^{-1}$. The present mass density is precisely predicted if the present time of the universe is given. We obtain ${\rho }_0=1.6\times 10^{-29}g.c{m}^{-3}$ for $t_0=1.5\times 10^{10}yr$. The universe shows the slowly decelerating expansion for the time-varying coupling function.

11 pages, LaTeX2e