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Recently, a model for an emergent gravity based on $SO(5)$ Yang-Mills actionin Euclidian 4-dimensional spacetime was proposed. In this work we provide some1 and 2-loops computations and show that the model can accommodate suitablepredicting values for the Newtonian constant. Moreover, it is shown that thetypical scale of the expected transition between the quantum and thegeometrodynamical theory is consistent with Planck scale. We also provide adiscussion on the cosmological constant problem.

Predicting Planck scale and Newtonian constant from a Yang-Mills gauge theory: 1 and 2-loops estimates