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 6 = 0 for the large enough coupling parameter ω . 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 φ = h φ i + O (1 /ω ) because of the presence of cosmological matter. The scalar field of a proper cosmological solution should have the asymptotic form φ = O ( ρ/ω ) and should converge to zero in the continuous limit ρ/ω → 0.