2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33751The 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 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= <ϕ> +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\to 0.13 pages, LaTeX2e. Submitted to Physical Review DGeneral Relativity and Quantum Cosmologytext