UNIVERSE, cilt.4, sa.7, 2018 (SCI-Expanded)
We discuss a possible scale of gravitational origin at around 10 MeV, or 10 12 cm, which arises in theMacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago. A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to theMacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that the existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10 12 cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with theMacDowell-Mansouri formalism; it provides a possible explanation for the factor of similar to 10120 multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1-2MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.