A Note on Energy-Momentum Conservation in Palatini Formulation of L(R) Gravity

TL;DR

This paper demonstrates that in the Palatini formulation of $L(R)$ gravity, the energy-momentum tensor remains covariantly conserved by establishing its equivalence to a specific Brans-Dicke theory.

Contribution

It shows the equivalence of Palatini $L(R)$ gravity to a Brans-Dicke theory with $ ext{}\omega=-3/2$, ensuring energy-momentum conservation.

Findings

Energy-momentum tensor is covariantly conserved in Palatini $L(R)$ gravity.

Palatini $L(R)$ gravity is equivalent to $ ext{ } ext{omega}=-3/2$ Brans-Dicke theory.

Abstract

By establishing that Palatini formulation of $L(R)$ gravity is equivalent to $\omega=-3/2$ Brans-Dicke theory, we show that energy-momentum tensor is covariantly conserved in this type of modified gravity theory.