Understand
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.