Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology

Abstract

We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds). There are analyzed alternatives to Einstein gravity (including theories with broken local Lorentz invariance) and shown how general relativity and modifications can be equivalently re-formulated in Finsler like variables. We focus on prospects in modern cosmology and Finsler acceleration of Universe. All known formalisms are outlined - anholonomic frames with associated nonlinear connection structure, the geometry of the Levi-Civita and Finsler type connections, all defined by the same metric structure, Einstein equations in standard form and/or with nonholonomic/ Finsler variables - and the following topics are discussed: motivation for Finsler gravity; generalized principles of equivalence and covariance; fundamental geometric/ physical structures; field equations and nonholonomic constraints; equivalence with other models of gravity and viability criteria. Einstein-Finsler gravity theories are elaborated following almost the same principles as in the general relativity theory but extended to Finsler metrics and connections. Gravity models with anisotropy can be defined on (co) tangent bundles or on nonholonomic pseudo-Riemannian manifolds. In the second case, Finsler geometries can be modelled as exact solutions in Einstein gravity. Finally, some examples of generic off-diagonal metrics and generalized connections, defining anisotropic cosmological Einstein-Finsler spaces are analyzed; certain criteria for Finsler accelerating evolution are analyzed.

latex 2e, v3 on 47 pages, accepted to IJMPD, new section 3.2.3 with additional references and discussions

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Cited by in corpus (52)

• Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Finsler gravity action from variational completion
• Finsler spacetime geometry in Physics
• The Finslerian wormhole models
• On the definition and examples of cones and Finsler spacetimes
• Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Cosmology of Lorentz fiber-bundle induced scalar-tensor theories
• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Berwald spacetimes and very special relativity
• Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions
• Dynamics in Varying vacuum Finsler-Randers Cosmology
• Finsler metrics and relativistic spacetimes
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Bounce cosmology in generalized modified gravities
• Standard static Finsler spacetimes
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
• Spacetime and observer space symmetries in the language of Cartan geometry
• CPT-Violating Leptogenesis induced by Gravitational Defects
• The Finslerian compact star model
• Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• On Finsler spacetimes with a timelike Killing vector field
• On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields
• Dual redshift on Planck-scale-curved momentum spaces
• Finsler-Randers-Sasaki gravity and cosmology
• Effective Einstein Cosmological Spaces for Non-Minimal Modified Gravity
• Off-Diagonal Ekpyrotic Scenarios and Equivalence of Modified, Massive and/or Einstein Gravity
• Dark Gravitational Sectors on a Generalized Scalar-Tensor Vector Bundle Model and Cosmological Applications
• Applications of the Schwarzschild-Finsler-Randers model
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Affine sphere relativity
• A geometric method of constructing exact solutions in modified f(R,T)-gravity with Yang-Mills and Higgs interactions
• Finslerian wormhole solution in the framework of modified gravity
• Equivalent off-diagonal cosmological models and ekpyrotic scenarios in f(R)-modified, massive and Einstein gravity
• Cosmic magnetization in curved and Lorentz violating space-times
• Relativistic Finsler geometry
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Modified Dynamical Supergravity Breaking and Off-Diagonal Super-Higgs Effects
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified Finsler Gravity
• Wormholes and Off-Diagonal Solutions in f(R,T), Einstein and Finsler Gravity Theories
• Observer dependent geometries
• Einstein Spaces Modeling Nonminimal Modified Gravity
• Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications
• Orthogonal Basis and Motion in Finsler Geometry
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity
• Orthonormal Basis in Minkowski Space