Cosmology Based on Finsler and Finsler-like Metric Structure of Gravitational Field

In this article, we review some aspects of gravitational field and cosmology based on Finsler and Finsler-like generalized metric structures. The geometrical framework of these spaces allows further investigation of locally-anisotropic phenomena related to the gravitational field and cosmological considerations, e.g the extracted geodesics, deflection of light, Finsler-Einstein gravitational field equations , the Friedmann equations and the Raychaudhuri equations include extra anisotropic terms that in the Riemannian framework of General Relativity (GR) are not interpreted. This approach gives us the opportunity to extend the research with more degrees of freedom on the tangent bundle of a spacetime manifold. In the above mentioned generalizations omitting the extra anisotropic terms we recover the framework of GR. In addition, we study the gravitational Magnus effect in a generalized metric framework. Based on this approach, we describe further properties of Finsler-Randers (FR) and Schwarzschild Finsler Randers (SFR) cosmological models which are useful for the description and evolution of the universe.