Modified gravity with arbitrary coupling between matter and geometry

TL;DR

This paper develops a generalized $f(R)$ gravity model with arbitrary matter-geometry coupling, deriving field equations, equations of motion, and analyzing the Newtonian limit and planetary precession effects.

Contribution

It introduces a new class of gravity models with arbitrary matter-geometry coupling and derives their field equations and test particle motion.

Findings

Test particles experience non-geodesic motion due to an extra force.

The model's Newtonian limit is analyzed.

Solar System observations constrain the magnitude of the extra force.

Abstract

The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the particular case in which the Lagrange density of the matter is an arbitrary function of the energy-density of the matter only. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the model is also considered. The perihelion precession of an elliptical planetary orbit in the presence of an extra force is obtained in a general form, and the magnitude of the extra gravitational effects is constrained in the case of a constant extra force by using Solar System observations.