Quantum Gravity and String Theory


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.

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Submission history

[v1] 2019-12-13 03:11:53
[v2] 2019-12-15 00:47:23

Unique-IP document downloads: 25 times

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