Palatini $f(R)$ gravity in the solar system: post-Newtonian equations of motion and complete PPN parameters

TL;DR

This paper analyzes Palatini $f(R)$ gravity in the solar system using post-Newtonian formalism, showing that the orbital dynamics are essentially the same as in general relativity, with some redefinitions affecting internal energy and pressure.

Contribution

It provides a detailed post-Newtonian analysis of Palatini $f(R)$ gravity, including non-spherical planets and non-analytical functions, extending previous work.

Findings

Center-of-mass orbits match general relativity after redefinitions.

Metric depends on additional terms beyond standard PPN potentials.

Redefinitions of internal energy and pressure are not constrained by solar system tests.

Abstract

We perform a post-Newtonian (PN) solar system analysis for Palatini $f(R)$ theories considering finite volume non-spherical planets and with emphasis to $f(R)$ functions that are analytical about $R=0$. First we consider the Will-Nordtvedt parametrized post-Newtonian (PPN) formalism, from which the metric is shown to depend, in general, on terms not covered by the standard PPN potentials. Hence, a full analysis of the PN equations of motion is performed. From the latter we conclude that, apart from redefinitions on the internal energy and the pressure, which cannot be constrained by solar system tests, the center-of-mass orbits are the same as in general relativity. We discuss further the physics of these redefinitions and use an argument to extend our analytical $f(R)$ results towards some non-analytical functions.