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)
$\omega$ 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
($\omega_{0}$ and $\omega_{a}$) 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 $\gamma$ and it can be
parameterized by $\gamma_{0} + \gamma_{a} (1 - a)$ in general. We use the
scalar-tensor theories of gravity (STG) and show that the discernment between
models is possible only when $\gamma_a$ 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 $\omega$ and
$\gamma$. From this method, we can rule out or prove the viable STG in future
observations. When we use $Z(\phi) =1$, $F$ shows the convex shape of evolution
in a viable STG model. The viable STG models with $Z(\phi) = 1$ are not
distinguishable from dark energy models when we strongly limit the solar system
constraint.
