# Solar System Tests of a New Class of $f(z)$ Theory

## TL;DR

This paper introduces a new $f(z)$ gravity model, constrains its parameters with cosmological data, tests it against solar system observations, and combines these constraints to reconstruct the $f(R)$ actions, offering a novel approach to alternative gravity theories.

## Contribution

It develops a method to test $f(z)$ gravity models using both cosmological and solar system data, and reconstructs the corresponding $f(R)$ actions, advancing the understanding of alternative gravity models.

## Key findings

- Cosmological data constrains the $f(z)$ model parameters.
- Solar system observations provide independent tests of the models.
- Combined constraints allow reconstruction of $f(R)$ actions.

## Abstract

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.