Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology

TL;DR

This paper explores the foundations and implications of Einstein-Finsler gravity theories, highlighting their potential in modern cosmology and the acceleration of the universe, by reformulating general relativity within Finsler geometric frameworks.

Contribution

It provides a comprehensive analysis of Finsler gravity theories, including their geometric structures, equivalence to Einstein gravity, and applications in cosmology and universe acceleration.

Findings

Finsler gravity can be formulated with metric compatible connections.

Finsler geometries can be modeled as solutions in Einstein gravity.

Criteria for Finsler-driven accelerated cosmological evolution are identified.

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.