General teleparallel gravity from Finsler geometry

Riemannian geometry, as a basis for general relativity, can be obtained from the more general Finsler geometry in terms of the Cartan connection and Chern connection, as discussed frequently in the literature. However, there are other gravity theories that can be made to be equivalent to general relativity but are based on non-Riemannian geometry. Famous examples are the Teleparallel and Symmetric Teleparallel gravity theories. In this paper, we show how to obtain the geometry for Teleparallel gravity from Finsler geometry in terms of a ‘Teleparallel type’ connection.

Para-CR Structures of Codimension 2 on Tangent Bundles in Riemann–Finsler Geometry

We determine a 2-codimensional para-CR structure on the slit tangent bundle T0 M of a Finsler manifold（M,F） by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f-structure.This condition is satisfied when（M,F） is of scalar flag curvature（particularly constant） or if the Riemannian manifold（M,g） is of constant curvature.

Adapted Metrics and Webster Curvature in Finslerian 2-Dimensional Geometry

The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.

Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity

Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

Constraints from Type Ia supernovae on the Λ-CDM model in Randers-Finsler space

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann equation and a new luminosity distance-redshift relation is proposed. A best-fit to the Type Ia supernovae （SNe） observations yields that the Λ in the Λ-CDM model is suppressed to almost zero. This fact indicates that the astronomical observations on the Type Ia SNe can be described well without invoking any form of dark energy. The best-fit age of the universe is given. It is in agreement with the age of our galaxy.

Towards a gravitation theory in Berwald-Finsler space

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by the Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric in general. This indicates that the local Lorentz invariance is violated.

Convergence of Finslerian metrics under Ricci flow

In this work,we study the convergence of evolving Finslerian metrics first in a general flow and next under Finslerian Ricci flow.More intuitively it is proved that a family of Finslerian metrics g（t）which are solutions to the Finslerian Ricci flow converges in C~∞ to a smooth limit Finslerian metric as t approaches the finite time T.As a consequence of this result one can show that in a compact Finsler manifold the curvature tensor along the Ricci flow blows up in a short time.

Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime

The WMAP and Planck observations show that the quadrupole and octopole orientations of the CMB might align with each other. We reveal that the quadrupole-octopole alignment is a natural implication of the primordial power spectrum in an anisotropic spacetime. The primordial power spectrum is presented with a dipolar modulation. We obtain the privileged plane by employing the ＂power tensor＂ technique. At this plane, there is maximum correlation between quadrupole and octopole. The probability for the alignment is much larger than that in the isotropic universe. We find that this model would lead to deviations from the statistical isotropy only for low-l multipoles.