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Scalar-Tensor Models of Normal and Phantom Dark Energy

We consider the viability of dark energy (DE) models in the framework of the scalar-tensor theory of gravity, including the possibility to have a phantom DE at small redshifts $z$ as admitted by supernova luminosity-distance data. For small $z$, the generic solution for these models is constructed in the form of a power series in $z$ without any approximation. Necessary constraints for DE to be phantom today and to cross the phantom divide line $p=-ρ$ at small $z$ are presented. Considering the Solar System constraints, we find for the post-Newtonian parameters that $γ_{PN}<1$ and $γ_{PN,0}\approx 1$ for the model to be viable, and $β_{PN,0}>1$ (but very close to 1) if the model has a significantly phantom DE today. However, prospects to establish the phantom behaviour of DE are much better with cosmological data than with Solar System experiments. Earlier obtained results for a $Λ$-dominated universe with the vanishing scalar field potential are extended to a more general DE equation of state confirming that the cosmological evolution of these models rule them out. Models of currently fantom DE which are viable for small $z$ can be easily constructed with a constant potential; however, they generically become singular at some higher $z$. With a growing potential, viable models exist up to an arbitrary high redshift.