Fully conservative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gravity and Solar System constraints
Nicolas R. Bertini, Hermano Velten
Abstract
The $f(R,T)$ gravity is a model whose action contains an arbitrary function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. We consider the minimally coupled model $f(R,T)=\ensuremath{\chi}(R)+\ensuremath{\varphi}(T)$ and shown that, for perfect fluids, the analysis of dynamical equations are sufficient to determine how $\ensuremath{\varphi}$ depends on $T$, independently of the matter fields equation of state and the geometry of space-time. Imposing the energy-momentum tensor conservation we obtain that the trace dependent part $\ensuremath{\varphi}$ must be linear in $T$, apart from the trivial case of a constant. However, the linear dependence on $T$ is severely constrained using the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism. The result of the PPN analysis is discussed and in addition it is shown that the diffeomorphism invariance of the matter action imposes strong constraints on conservative versions of $f(R,T)$ gravity.