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I do not agree with the authors of papers arXiv:0806.2184 andarXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 andB676 (2009) 173). They consider that \textit{"In Finsler manifold, there existsa unique linear connection - the Chern connection ... It is torsion freenessand metric compatibility ... "}. There are well known results (for example,presented in monographs by H. Rund and R. Miron and M. Anastasiei) that inFinsler geometry there exist an infinite number of linear connections definedby the same metric structure and that the Chern and Berwald connections\textbf{are not metric compatible.} For instance, the Chern's one (being withzero torsion and "weak" compatibility on the base manifold of tangent bundle)is not generally compatible with the metric structure on total space. Thisresults in a number of additional difficulties and sophistication in definitionof Finsler spinors and Dirac operators and in additional problems with furthergeneralizations for quantum gravity and noncommutative/string/brane/gaugetheories. I conclude that standard physics theories can be generalizednaturally by gravitational and matter field equations for the Cartan and/or anyother Finsler metric compatible connections. This allows us to construct morerealistic models of Finsler spacetimes, anisotropic field interactions andcosmology.

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