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We consider a generalized scalar–tensor theory, where we let the coupling function ω(ϕ) and the effective cosmological constants Λ(ϕ) be undetermined. We obtain general expressions for ω(ϕ) and Λ(ϕ) in terms of the scalar field and the scale factor, and show that ω(ϕ) depends on the scalar field and the scale factor in a complicated way. In order to study the conditions for an accelerated expansion at the present time and a decelerated expansion in the past, we assume a power law evolution for the scalar field and the scale factor. We analyze the required conditions that allow our model to satisfy the weak field limits on ω(ϕ), and at the same time, to obtain the correct values of cosmological parameters, as the energy density Ω m0 and cosmological constant Λ(t 0 ). We also study the conditions for a decelerated expansion at an early time dominated by radiation. We find values for ω(ϕ) and Λ(ϕ) consistent with the expectations of a where the cosmological constant decreases with the time and the coupling function increases until the values are accepted today.
Díaz-Rivera et al. (Mon,) studied this question.