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

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 separable model $f(R,T)=\chi (R)+\phi (T)$ and shown that, for perfect fluids, the dynamical equations are sufficient to determine how $\phi$ depends on $T$, independently of the matter state equation and the geometry of space-time. Imposing the energy-momentum tensor conservation we obtain that $\phi$ must be linear in $T$. However, the $T$ dependence is severely constrained using the full Will-Nordtvedt version of the parameterized 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.

arXiv comment15 pages, thirteen references added and text improvements. Typos corrected. Accepted in PRD

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Cited by in corpus (9)

• Observational constraints on the equation of state of viscous fluid in $f(R,T)$ gravity
• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• Growth of cosmic perturbations in the modified $f(R,T)$ gravity
• Cosmological Study in Myrzakulov $F(R,T)$ Quasi-dilaton Massive Gravity
• Modified $f(R,T)$ theory in light of gravitational wave standard sirens
• White dwarf cooling in $f(R,T)$ gravity
• Wormhole Solutions and Pre-inflationary Epoch in $F(R,T)$ Gravity with Axion Fields
• Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars
• Intermediate Coupling Regime in Dilatonic $f(R,T)$ Inflationary Universe