Palatini formulation of modified gravity with a nonminimal curvature-matter coupling

Abstract

We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity.

7 pages, no figures; v2, revised and corrected version; new Section added

References in corpus (28)

• Dynamics of dark energy
• Extra force in $f(R)$ modified theories of gravity
• Low surface brightness galaxies rotation curves in the low energy limit of $R^n$ gravity : no need for dark matter?
• Nonminimal coupling of perfect fluids to curvature
• Modified gravity with arbitrary coupling between matter and geometry
• Dark matter as a geometric effect in f(R) gravity
• Bimetric MOND gravity
• The matter power spectrum in f(R) gravity
• Analysis of Rotation Curves in the framework of R^n gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• A viability criterion for modified gravity with an extra force
• Thin accretion disks in f(R) modified gravity models
• Do f(R) theories matter?
• On the non-minimal gravitational coupling to matter
• Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
• Dark matter and dark energy as a effects of Modified Gravity
• The viability of theories with matter coupled to the Ricci scalar
• Constraints on f(R) Cosmology in the Palatini Formalism
• Viable Palatini-f(R) cosmologies with generalized dark matter
• Dynamical Aspects of Generalized Palatini Theories of Gravity
• Curvature singularities, tidal forces and the viability of Palatini f(R) gravity
• Re-examination of Polytropic Spheres in Palatini f(R) Gravity
• Motion of test bodies in theories with nonminimal coupling
• Equivalence between Palatini and metric formalisms of f(R)-gravity by divergence free current
• Gödel-type universes in Palatini f(R) gravity
• Geodesic Congruences in the Palatini f(R) Theory
• Palatini f(R) gravity as a fixed point

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• Generalized curvature-matter couplings in modified gravity
• Wormholes supported by hybrid metric-Palatini gravity
• Cosmology of hybrid metric-Palatini f(X)-gravity
• Extended $f(R,L_m)$ gravity with generalized scalar field and kinetic term dependences
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Generalized dark gravity
• Cosmology with Hu-Sawicki gravity in Palatini Formalism