Required Conditions for Late Time Acceleration and Early Time Deceleration in Generalized Scalar-Tensor Theories
We consider a generalized scalar-tensor theory, where we let the coupling function $ω(ϕ)$ and the effective cosmological constants $Λ(ϕ)$ 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 analyse 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 theory where the cosmological constant decreases with the time and the coupling function increases until the values accepted today.