(Non-) geodesic motion in chameleon Brans Dicke model

TL;DR

This paper investigates how different types of matter move in a chameleon Brans-Dicke model with non-minimal coupling, revealing conditions under which their motion is geodesic or non-geodesic.

Contribution

It analyzes the motion of various matter fields in a non-minimally coupled Brans-Dicke theory, highlighting when their trajectories follow geodesics or deviate from them.

Findings

Massless scalar and photon follow null geodesics only at high frequencies.

Dust and perfect fluid are geodesic for L_m = -P and non-geodesic for L_m = R.

Point particles exhibit non-geodesic motion.

Abstract

Based on \cite{16}, we assume there is a non-minimal coupling between the scalar field and matter in Brans-Dicke model. We analyzes the motion of different matter such as, massless scalar field, photon, massless perfect fluid (dust), massive perfect fluid and point particle matter in this theory. We show that the motion of massless scalar field and photon can satisfy null geodesic motion only in high frequency limit. Also we find that the motion of the dust and massive perfect fluid is geodesic for $L_m=-P$ and is non-geodesic for $L_m=\R$. Finally, we study the motion of point particle and show that the motion of this kind of matter is non-geodesic.