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Constraints on scalar-tensor theories of gravity from observations

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) $ω$ for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called Chevallier-Polarski-Linder (CPL) parametrization where two parameters of it ($ω_{0}$ and $ω_{a}$) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter $γ$ and it can be parameterized by $γ_{0} + γ_{a} (1 - a)$ in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when $γ_a$ is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of $ω$ and $γ$. From this method, we can rule out or prove the viable STG in future observations. When we use $Z(ϕ) =1$, $F$ shows the convex shape of evolution in a viable STG model. The viable STG models with $Z(ϕ) = 1$ are not distinguishable from dark energy models when we strongly limit the solar system constraint.