On the Geometric Unification of Gravity and Dark Energy

E Koorambas

doi:10.1007/s10773-012-1162-2

Abstract

In the framework of Finslerian geometry, we propose a geometric unification between traditional gauge treatments of gravity, represented by a metric field, and dark energy, which arises as a corresponding gauge potential from the single SU(2) group. Furthermore, we study the perturbation of gravitational waves caused by dark energy. This proposition may have far reaching applications in astrophysics and cosmology.

Highlights

Observations of type Ia supernovae and of large-scale structure (LSS), in combination with measurements of the characteristic angular size of fluctuations in the cosmic microwave background (CMB)([1],[2],[3],[4],[5],[6],[7],[8],[9],[10]) provide evidence that the expansion of the Universe is accelerating
In the framework of Finslerian geometry, we propose a geometric unification between traditional gauge treatments of gravity, represented by metric field, and dark energy, which arises as a corresponding gauge potential from the single SU (2) group
We demonstrate that the dark energy would result naturally as a geometric effect of Finsler space, rather than being an additional suggestion

Summary

Introduction

Observations of type Ia supernovae and of large-scale structure (LSS), in combination with measurements of the characteristic angular size of fluctuations in the cosmic microwave background (CMB)([1],[2],[3],[4],[5],[6],[7],[8],[9],[10]) provide evidence that the expansion of the Universe is accelerating. The dark energy may result from Einstein’s cosmological constant (which has a phenomenally small value); from evolving scalar fields ([12]); and from a weakening of gravity in our 3 + 1 dimensions by leaking into the higher dimensions, as required in string theories ([13]). These explanations may have crucial borader implications on fundamental physics. 2. On the Finslerian geometric unification of gravity and dark energy In the framework of a Riemannian approach, where two nearby particles are subject to the traditional gravitational field g (free-falling), the Equation of Deviations of Geodesics (EDG) takes the form: D2n ds. B-field of dark energy is obtained by introducing the Lorentz term into the geodesics equation (1) and replacing the four-acceleration a du by D u a

D B ds u

Conclusion