## Born's Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant

**Authors:** Carlos Castro

The main features of how to build a Born's Reciprocal Gravitational
theory in curved phase-spaces are developed. The scalar curvature of the
8D cotangent bundle (phase space) is explicitly evaluated and a generalized
gravitational action in 8D is constructed that yields the observed
value of the cosmological constant and the Brans-Dicke-Jordan Gravity
action in 4D as two special cases. It is found that the geometry of the
momentum space can be linked to the observed value of the cosmological
constant when the curvature in momentum space is very large, namely
the small size of P is of the order of (1/R_{Hubble}). More general 8D actions
can be developed that involve sums of 5 distinct types of torsion squared
terms and 3 distinct curvature scalars R,P, S. Finally we develop a Born's
reciprocal complex gravitational theory as a local gauge theory in 8D of
the deformed Quaplectic group that is given by the semi-direct product
of U(1, 3) with the deformed (noncommutative) Weyl-Heisenberg group
involving four noncommutative coordinates and momenta. The metric is
complex with symmetric real components and antisymmetric imaginary
ones. An action in 8D involving 2 curvature scalars and torsion squared
terms is presented.

**Comments:** 23 pages, submitted to Foundations of Physics

**Download:** **PDF**

### Submission history

[v1] 3 Jul 2011

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