The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry

Abstract

We show that in modified $f(R)$ type gravity models with non-minimal coupling between matter and geometry, both the matter Lagrangian, and the energy-momentum tensor, are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with non-minimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra-force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is non-zero in the case of a fluid of dust particles.

6 pages, accepted for publication in PRD; references added

References in corpus (41)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Extra force in $f(R)$ modified theories of gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• Are f(R) dark energy models cosmologically viable ?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Solar System constraints to general f(R) gravity
• Nonminimal coupling of perfect fluids to curvature
• The Cosmology of Modified Gauss-Bonnet Gravity
• Modified gravity with arbitrary coupling between matter and geometry
• Limit to General Relativity in f(R) theories of gravity
• The Newtonian Limit of F(R) gravity
• Energy conditions in f(R)-gravity
• Dark energy and dark matter as curvature effects
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Dark matter as a geometric effect in f(R) gravity
• Solar System tests DO rule out 1/R gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• Spherical symmetry in $f(R)$-gravity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• The evolution of density perturbations in f(R) gravity
• Analysis of Rotation Curves in the framework of R^n gravity
• Dark energy from modified F(R)-scalar-Gauss-Bonnet gravity
• A viability criterion for modified gravity with an extra force
• Newton law corrections and instabilities in $f(R)$ gravity with the effective cosmological constant epoch
• Thin accretion disks in f(R) modified gravity models
• Do f(R) theories matter?
• Generalized virial theorem in f(R) gravity
• Constraining f(R) theories with the energy conditions
• On the non-minimal gravitational coupling to matter
• f(R) Gravity with Torsion: The Metric-Affine Approach
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Dark matter and dark energy as a effects of Modified Gravity
• The viability of theories with matter coupled to the Ricci scalar
• Viable Palatini-f(R) cosmologies with generalized dark matter
• The evolution of cosmological gravitational waves in f(R) gravity
• Motion of test bodies in theories with nonminimal coupling

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• Neutron stars in $f(\mathtt{R},{\mathtt{L}}_{\mathtt{m}})$ gravity with realistic equations of state: joint-constrains with GW170817, massive pulsars, and the PSR J0030+0451 mass-radius from $NICER$ data
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• Cosmology with Hu-Sawicki gravity in Palatini Formalism
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• Lagrangian description of cosmic fluids: mapping dark energy into unified dark energy
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• Maximum mass limit of strange stars in quadratic curvature-matter coupled gravity
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field