Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
arXiv:1903.12521 · doi:10.1088/1361-6382/aab27f
Abstract
We study field equations for a weak anisotropic model on the tangent Lorentz bundle of a spacetime manifold. A geometrical extension of General Relativity (GR) is considered by introducing the concept of local anisotropy, i.e. a direct dependence of geometrical quantities on observer velocity. In this approach, we consider a metric on as the sum of an h-Riemannian metric structure and a weak anisotropic perturbation, field equations with extra terms are obtained for this model. As well, extended Raychaudhuri equations are studied in the framework of Finsler-like extensions. Canonical momentum and mass-shell equation are also generalized in relation to their GR counterparts. Quantization of the mass-shell equation leads to a generalization of the Klein-Gordon equation and dispersion relation for a scalar field. In this model the accelerated expansion of the universe can be attributed to the geometry itself. A cosmological bounce is modeled with the introduction of an anisotropic scalar field. Also, the electromagnetic field equations are directly incorporated in this framework.
arXiv comment31 pages
References in corpus (46)
- Lorentz-Violating Extension of the Standard Model
- CPT Violation and the Standard Model
- Data Tables for Lorentz and CPT Violation
- Gravity, Lorentz Violation, and the Standard Model
- Very Special Relativity
- CPT and Lorentz Tests in Hydrogen and Antihydrogen
- General Very Special Relativity is Finsler Geometry
- Riemann-Finsler geometry and Lorentz-violating kinematics
- Finsler geometric extension of Einstein gravity
- The General Very Special Relativity in Finsler Cosmology
- Bipartite Riemann-Finsler geometry and Lorentz violation
- Causal structure and electrodynamics on Finsler spacetimes
- Resembling dark energy and modified gravity with Finsler-Randers cosmology
- Classical kinematics for Lorentz violation
- Friedmann Robertson-Walker model in generalised metric space-time with weak anisotropy
- Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
- Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
- Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity
- Classical-physics applications for Finsler space
- Light cones in Finsler spacetime
- Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
- Imperfect fluids, Lorentz violations and Finsler Cosmology
- Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
- Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis
- On the interplay between Lorentzian Causality and Finsler metrics of Randers type
- Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
- Covariant kinematics and gravitational bounce in Finsler space-times
- Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
- Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
- Finsler pp-waves
- Bi-metric pseudo-Finslerian spacetimes
- Weak Gravitational Field in Finsler-Randers Space and Raychaudhuri Equation
- Raychaudhuri equation and singularity theorems in Finsler spacetimes
- Standard static Finsler spacetimes
- Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
- On General Solutions of Einstein Equations
- Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
- On Fermat's principle for causal curves in time oriented Finsler spacetimes
- Decoupling of Field Equations in Einstein and Modified Gravity
- Finsler geometric perspective on the bulk flow in the universe
- New Classes of Off-Diagonal Cosmological Solutions in Einstein Gravity
- Cosmic magnetization in curved and Lorentz violating space-times
- Some physical displays of the space anisotropy relevant to the feasibility of its being detected at a laboratory
- Volume forms for time orientable Finsler spacetimes
- Focusing of world-lines in Weyl gravity
- Covariant kinematics of light in media and a generalized Raychaudhuri equation
Cited by in corpus (22)
- Backgrounds in gravitational effective field theory
- Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields
- Cosmological Finsler Spacetimes
- Observational constraints on Myrzakulov gravity
- Cosmology of Lorentz fiber-bundle induced scalar-tensor theories
- Cosmological applications of Myrzakulov gravity
- Dynamics in Varying vacuum Finsler-Randers Cosmology
- Bounce cosmology in generalized modified gravities
- Searches for beyond-Riemann gravity
- Schwarzschild-like solutions in Finsler-Randers gravity
- Finsler-Randers-Sasaki gravity and cosmology
- Exact Cosmology in Myrzakulov Gravity
- Dynamical system analysis of Myrzakulov gravity
- On the analyticity of static solutions of a field equation in Finsler gravity
- Dark Gravitational Sectors on a Generalized Scalar-Tensor Vector Bundle Model and Cosmological Applications
- Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
- Applications of the Schwarzschild-Finsler-Randers model
- Transit cosmological models in Myrzakulov F(R,T) gravity theory
- Gravitational Field on the Lorentz Tangent Bundle: Generalized Paths and Field Equations
- Anisotropic Conformal Dark Gravity on the Lorentz Tangent Bundle Spacetime
- Raychaudhuri equations, Tidal forces and Weak field Limit in Schwarzshild-Finsler-Randers spacetime
- Birkhoff Theorem for Berwald Finsler spacetimes