标题： 马赫的宇宙学解在广义标量-张量引力理论中 显示英文标题

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

摘要： 满足$\phi =O(\rho /\omega)$的 Machian 宇宙学解被讨论，用于具有完美流体（负压）的均匀各向同性宇宙，在广义标量-张量引力理论中。 我们提出$\omega (\phi)=\eta /(\xi -2)$作为 Machian 观点中的耦合函数。 参数$\xi$由于宇宙中物质的物理演化，随时间非常缓慢地从$\xi =0$变化到$\xi =2$。 当$\xi \to 2$时，耦合函数发散到$-\infty$，标量场$\phi$收敛到$G_{\infty}^{-1}$。 如果给定宇宙的当前时间，当前的质量密度可以被精确预测。 我们得到$\rho_{0}=1.6\times 10^{-29} g.cm^{-3}$对于$t_{0}=1.5\times 10^{10} yr$。 对于时变耦合函数，宇宙表现出缓慢的减速膨胀。 显示英文摘要

摘要： The Machian cosmological solution satisfying $\phi =O(\rho /\omega)$ 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 $\omega (\phi)=\eta /(\xi -2)$ 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 $\phi$ converges to $G_{\infty}^{-1}$. The present mass density is precisely predicted if the present time of the universe is given. We obtain $\rho_{0}=1.6\times 10^{-29} g.cm^{-3}$ for $t_{0}=1.5\times 10^{10} yr$. The universe shows the slowly decelerating expansion for the time-varying coupling function.