Solar System Experiments and the Interpretation of Saa’s Model of Gravity with Propagating Torsion as a Theory with Variable Plank ”Constant”

It is shown that the recently proposed interpretation of the transposed equi-affine theory of gravity as a theory with variable Plank ”constant” is inconsistent with basic solar system gravitational experiments. Recently a new model of gravity involving propagating torsion was proposed by A. Saa [1]-[5]. In this model a special type of Einstein-Cartan geometry is considered in which the usual volume element √−g dx is replaced with new one: e √−g dx – covariantly constant with respect to the transposed affine connection ∇T , hence the name transposed-equi-affine theory of gravity [6]. As a result the torsion vector Sα = Sαβ α turns to be potential: Sα = ∂αΘ, Θ being its scalar potential . Because of the exponential factor e in the volume element Saa’s model has a very important feature: it leads to a consistent application of the minimal E-mail: [email protected] Permanent address: Department of Theoretical Physics, Faculty of Physics, Sofia University, 5 James Bourchier Boulevard, Sofia 1164, Bulgaria E-mail: [email protected] We use the Schouten’s normalization conventions [7] which differs from the original ones in [1]–[5].