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 (53)

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• Resembling dark energy and modified gravity with Finsler-Randers cosmology
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• Finsler spacetime geometry in Physics
• The Finslerian wormhole models
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• 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
• Berwald spacetimes and very special relativity
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• Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions
• Dynamics in Varying vacuum Finsler-Randers Cosmology
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Finsler metrics and relativistic spacetimes
• Bounce cosmology in generalized modified gravities
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• Spacetime and observer space symmetries in the language of Cartan geometry
• CPT-Violating Leptogenesis induced by Gravitational Defects
• The Finslerian compact star model
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• Extensions of Lorentzian spacetime geometry: From Finsler to Cartan and vice versa
• 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
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• Dark Gravitational Sectors on a Generalized Scalar-Tensor Vector Bundle Model and Cosmological Applications
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