General approach to the Lagrangian ambiguity in $f(R,T)$ gravity

Abstract

The $f(R,T)$ gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, $R$, and the trace of the stress-energy tensor, $T$; its field equations also depend on matter Lagrangian, ${\mathcal{L}}_m$. In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the ${\mathcal{L}}_m$ dependence from $f(R,T)$ gravity field equations by generalizing the approach of Moraes [Eur. Phys. J. C 79(8), 674 (2019)]. We also propose a general approach where we argue that the trace of the energy-momentum tensor must be considered an "unknown" variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy-momentum tensor of the $f(R,T)$ gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

arXiv commentNew section added with application to Cosmology. Matches the published version

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Cited by in corpus (19)

• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Quark stars with 2.6 $M_{\odot }$ in a non-minimal geometry-matter coupling theory of gravity
• Thermodynamics and Perturbative Analysis of Some Newly Developed $\mathcal{F}(R,L_m,T)$ Theories Under the Scenario of Conserved Energy-momentum Tensor
• Traversable wormholes in the traceless $f(R,T)$ gravity
• Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory
• Effects of the matter Lagrangian degeneracy in $f(Q,T)$ gravity
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• Growth of cosmic perturbations in the modified $f(R,T)$ gravity
• NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
• Thermodynamics of a Non-canonical $f(\bar{R},\bar{T})$ gravity
• Modified $f(R,T)$ theory in light of gravitational wave standard sirens
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• Dynamical Wormhole Solutions in $f(R,T)$ Gravity
• White dwarf cooling in $f(R,T)$ gravity
• Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars
• Energy Conditions and Stability of Charged Wormholes in $f(R,{\mathcal{L}}_m)$ Gravity: A Comparative Analysis with Compact Objects
• A MOND model applied to the rotation curve of galaxies
• Structure of Anisotropic Magnetized Neutron Stars in f(R,T) Gravity with Realistic Equation of State