Solar System Tests of a New Class of $f(z)$ Theory
  Recently, a new kind of $f(z)$ theory is proposed to provide a different
perspective for the development of reliable alternative models of gravity in
which the $f(R)$ Lagrangian terms are reformulated as polynomial
parameterizations $f(z)$. In the previous study, the parameters in the $f(z)$
models have been constrained by using cosmological data. In this paper, these
models will be tested by the observations in the solar system. After solving
the Ricci scalar as a function of the redshift, one could obtain $f(R)$ that
could be used to calculate the standard Parameterized-Post-Newtonian (PPN)
parameters. First, we fit the parametric models with the latest cosmological
observational data. Then the tests are performed by solar system observations.
And last we combine the constraints of solar system and cosmology together and
reconstruct the $f(R)$ actions of the $f(z)$ parametric models.
