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