Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li

Abstract

I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 and B676 (2009) 173). They consider that \textit{"In Finsler manifold, there exists a unique linear connection - the Chern connection ... It is torsion freeness and metric compatibility ... "}. There are well known results (for example, presented in monographs by H. Rund and R. Miron and M. Anastasiei) that in Finsler geometry there exist an infinite number of linear connections defined by the same metric structure and that the Chern and Berwald connections \textbf{are not metric compatible.} For instance, the Chern's one (being with zero torsion and "weak" compatibility on the base manifold of tangent bundle) is not generally compatible with the metric structure on total space. This results in a number of additional difficulties and sophistication in definition of Finsler spinors and Dirac operators and in additional problems with further generalizations for quantum gravity and noncommutative/string/brane/gauge theories. I conclude that standard physics theories can be generalized naturally by gravitational and matter field equations for the Cartan and/or any other Finsler metric compatible connections. This allows us to construct more realistic models of Finsler spacetimes, anisotropic field interactions and cosmology.

latex2e, 11pt, 13 pages, v2 with updated references and typos corrections, accepted to Phys. Lett. B

References in corpus (14)

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Cited by in corpus (12)

• The Finslerian wormhole models
• Light cones in Finsler spacetime
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
• Cosmological evolution and dark energy in osculating Barthel-Randers geometry
• Cosmological tests of the osculating Barthel-Kropina dark energy model
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_m)$ gravity
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
• Spinning Equations for Objects of Some Classes in Finslerian Geometry
• Nonholonomic Clifford and Finsler Structures, Non-Commutative Ricci Flows, and Mathematical Relativity