Physical Significance of the Difference between the Brans-Dicke Theory and General Relativity

The asymptotic behavior of the scalar field and its physical meaning are discussed for T=0 and T\neq 0 for the large enough coupling parameter \omega. The special character of the Brans-Dicke theory is also discussed for local and cosmological problems in comparison with general relativity and the selection rules are introduced respectivley. The scalar field by locally-distributed matter should exhibit the asymptotic behavior \phi = <\phi> +O(1/\omega) because of the presence of cosmological matter. The scalar field of a proper cosmological solution should have the asymptotic form \phi =O(\rho /\omega) and should converge to zero in the continuous limit \rho /\omega \to 0.