On the non-minimal gravitational coupling to matter

Abstract

The connection between $f(R)$ theories of gravity and scalar-tensor models with a "physical" metric coupled to the scalar field is well known. In this work, we pursue the equivalence between a suitable scalar theory and a model that generalises the $f(R)$ scenario, encompassing both a non-trivial scalar curvature term and a non-minimum coupling of the scalar curvature and matter. This equivalence allows for the calculation of the PPN parameters $\beta$ and $\gamma$ and, eventually, a solution to the debate concerning the weak-field limit of $f(R)$ theories.

11 pages

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Cited by in corpus (67)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R,T) gravity
• f(R,L_m) gravity
• Generalized curvature-matter couplings in modified gravity
• Wormhole geometries supported by a nonminimal curvature-matter coupling
• The Lagrangian description of perfect fluids and modified gravity with an extra force
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• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
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• Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
• Energy Conditions in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• Palatini formulation of modified gravity with a nonminimal curvature-matter coupling
• Reheating via a generalized non-minimal coupling of curvature to matter
• Initial and final de Sitter universes from modified $f(R)$ gravity
• Recovering a MOND-like acceleration law in mimetic gravity
• Mimicking dark matter through a non-minimal gravitational coupling with matter
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• Anisotropic Fluid and Bianchi Type III Model in f(R) Gravity
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• Modified Friedmann Equation from Nonminimally Coupled Theories of Gravity
• The correspondence between a scalar field and an effective perfect fluid
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• Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature
• Conditions and instability in $f(R)$ gravity with non-minimal coupling between matter and geometry
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• Baryogenesis in Nonminimally Coupled $f(R)$ Theories
• Unimodular $f(R,T)$ Gravity
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• Dynamical analysis of nonminimal coupled theories
• A new shape function for wormholes in $f(R)$ gravity and General Relativity
• The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
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• Magnetofluid Dynamics in curved spacetime
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• Motion of pole-dipole and quadrupole particles in non-minimally coupled theories of gravity
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• Singularity problem in f(R) model with non-minimal coupling
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• Gravitational wave polarizations in nonminimally coupled gravity
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