2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33830The Machian cosmological solution satisfying $ϕ=O(ρ/ω)$ in the generalized scalar-tensor theory of gravitation with the varying cosmological constant is summarized. The scalar field $ϕ$ with the exponential potential is introduced as dark matter and the barotropic evolution of matter in the universe is discussed. As the universe expands, the coefficient $γ$ of the equation of state approaches to -1/3 and the coupling function $ω(ϕ)$ diverges to $-\infty $.7 pages, LaTeX2eGeneral Relativity and Quantum Cosmologytext