## Born's Reciprocal Relativity Theory, Curved Phase Space, Finsler Geometry and the Cosmological Constant

**Authors:** Carlos Castro

A brief introduction of the history of Born's Reciprocal Relativity Theory, Hopf algebraic deformations of the Poincare algebra, de Sitter algebra, and noncommutative spacetimes
paves the road for the exploration of gravity in $curved$ phase spaces within the context of the
Finsler geometry of the cotangent bundle $T^* M$ of spacetime. A scalar-gravity model is duly studied, and exact nontrivial analytical solutions
for the metric and nonlinear connection are found that
obey the generalized gravitational field equations, in addition to satisfying the $zero$ torsion conditions
for $all$ of the torsion components. The $curved$ base spacetime manifold and internal momentum space both turn out to be (Anti) de Sitter type. The most salient feature is that the solutions capture the very early inflationary and very-late-time de Sitter phases of the Universe. A $regularization$ of the $8$-dim phase space action leads naturally to an extremely small effective cosmological constant $ \Lambda_{eff}$, and which in turn, furnishes an extremely small value for the underlying four-dim spacetime cosmological constant $ \Lambda$, as a direct result of a $correlation$ between $ \Lambda_{eff} $ and $ \Lambda$ resulting from the field equations. The rich structure of Finsler geometry deserves to be explore further since it can shine some light into Quantum Gravity, and lead to interesting cosmological phenomenology.

**Comments:** 18 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-12-13 03:11:53

[v2] 2019-12-15 00:47:23

**Unique-IP document downloads:** 25 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*