f(R) gravity with torsion: a geometric approach within the J-bundles framework

Abstract

We discuss the f(R)-theories of gravity with torsion in the framework of jet-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber jet-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang--Mills fields and spin perfect fluid. Such fields enlarge the jet-bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories.

17 pages

References in corpus (10)

• Dynamics of dark energy
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Reconciling dark energy models with f(R) theories
• On Physical Equivalence between Nonlinear Gravity Theories
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• f(R) Gravity with Torsion: The Metric-Affine Approach
• Conformal aspects of Palatini approach in Extended Theories of Gravity
• Dark energy models toward observational tests and data
• A first-order purely frame-formulation of General Relativity
• A vielbein formulation of unified Einstein-Maxwell theory

Cited by in corpus (25)

• Extended Theories of Gravity
• f(T) teleparallel gravity and cosmology
• Flag-Dipole Spinor Fields in ESK Gravities
• The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter
• f(R) cosmology with torsion
• The mass-radius relation for neutron stars in $f(R)=R+\alpha R^2$ gravity: a comparison between purely metric and torsion formulations
• Dirac spinors in Bianchi-I f(R)-cosmology with torsion
• Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field
• Metric-affine $f(R)$-gravity with torsion: an overview
• Dirac fields in f(R)-gravity with torsion
• The most general ELKO Matter in torsional f(R)-theories
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• Deriving the mass of particles from Extended Theories of Gravity in LHC era
• On the junction conditions in $f(R)$-gravity with torsion
• Testing metric-affine f(R)-gravity by relic scalar gravitational waves
• A review about Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry
• Running coupling in electroweak interactions of leptons from f(R)-gravity with torsion
• The Affine Structure of Gravitational Theories: Symplectic Groups and Geometry
• Maxwell extension of $f(R)$ gravity
• The gauge symmetries of f(R) gravity with torsion in the Cartan formalism
• Spin fluids in Bianchi-I f(R)-cosmology with torsion
• Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory
• Weak Forces and Neutrino Oscillations under the standards of Hybrid Gravity with Torsion
• Two-Component Spinors in Spacetimes with Torsionful Affinities
• Robustness of predicted CMB fluctuations in Cartan $F(R)$ gravity