Varying Cosmological Constant and the Machian Solution in the Generalized ScalarTensor Theory
Abstract
The cosmological constant $(1/2)\lambda_{1}\phi_{, \mu}\phi ^{, \mu}/\phi ^{2}$ is introduced to the generalized scalartensor theory of gravitation with the coupling function $\omega (\phi)=\eta /(\xi 2)$ and the Machian cosmological solution satisfying $\phi =O(\rho /\omega)$ is discussed for the homogeneous and isotropic universe with a perfect fluid (with negative pressure). We require the closed model and the negative coupling function for the attractive gravitational force. The constraint $% \omega (\phi)<3/2$ for $0\leqq \xi <2$ leads to $\eta >3$. If $\lambda_{1}<0$ and $0\leqq \eta /\lambda_{1}<2$, the universe shows the slowly accelerating expansion. The coupling function diverges to $\infty $ and the scalar field $\phi $ converges to $G_{\infty}^{1}$ when $\xi \to 2$ ($t\to +\infty $). The cosmological constant decays in proportion to $t^{2}$. Thus the Machian cosmological model approaches to the Friedmann universe in general relativity with $\ddot{a}=0$, $\lambda =0$, and $p=\rho /3$ as $t\to +\infty $. General relativity is locally valid enough at present.
 Publication:

arXiv eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:grqc/0103003
 Bibcode:
 2001gr.qc.....3003M
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 10 pages, LaTeX2e