Fully conservative $f(R,T)$ gravity and Solar System constraints

• DOI: 10.48550/arxiv.2303.09699
• Publication Date: 2023-01-01
• Authors: Nicolas R. Bertini; Hermano Velten
• Keywords: Diffeomorphism; Stress–energy tensor; f(R) gravity

The $f(R,T)$ gravity is a model whose action contains an arbitrary function of the Ricci scalar $R$ and trace energy-momentum tensor $T$. We consider separable $f (R, T ) = χ(R) + φ(T )$ shown that, for perfect fluids, dynamical equations are sufficient to determine how $φ$ depends on $T$, independently matter state equation geometry space-time. Imposing conservation we obtain that must be linear in However, $T$ dependence severely constrained using full Will-Nordtvedt version parameterized post-Newtonian (PPN) formalism. result PPN analysis discussed addition it diffeomorphism invariance imposes strong constraints conservative versions gravity.