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/RHubble). 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
[v1] 3 Jul 2011
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