The paper by Tiberiu Harko, Francisco S. N. Lobo, Shin'ichi Nojiri, and Sergei D. Odintsov explores modified theories of gravity, specifically focusing on the $f(R, T)$ gravity model, where the gravitational Lagrangian depends on both the Ricci scalar $R$ and the trace of the stress-energy tensor $T$. The authors derive the gravitational field equations and the equations of motion for test particles in this framework. They discuss several particular models, including scalar field models, and analyze the cosmological implications of $f(R, T^0)$ models, where $T^0$ is the trace of the stress-energy tensor of a self-interacting scalar field. The motion of massive test particles is shown to be non-geodesic due to an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and constraints on the magnitude of the extra-acceleration are derived using the perihelion precession of Mercury. The paper concludes with a discussion on the potential differences and signatures of $f(R, T)$ gravity compared to standard general relativity in various astrophysical and cosmological contexts.The paper by Tiberiu Harko, Francisco S. N. Lobo, Shin'ichi Nojiri, and Sergei D. Odintsov explores modified theories of gravity, specifically focusing on the $f(R, T)$ gravity model, where the gravitational Lagrangian depends on both the Ricci scalar $R$ and the trace of the stress-energy tensor $T$. The authors derive the gravitational field equations and the equations of motion for test particles in this framework. They discuss several particular models, including scalar field models, and analyze the cosmological implications of $f(R, T^0)$ models, where $T^0$ is the trace of the stress-energy tensor of a self-interacting scalar field. The motion of massive test particles is shown to be non-geodesic due to an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and constraints on the magnitude of the extra-acceleration are derived using the perihelion precession of Mercury. The paper concludes with a discussion on the potential differences and signatures of $f(R, T)$ gravity compared to standard general relativity in various astrophysical and cosmological contexts.