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My intuitive picture of how gravity works is essentially based on the ‘space’ part of Einstein’s gravitational field equations which tell me that presence of matter/energy produces Ricci curvature.  So consider $M_t$ to be the physical universe parametrized by time as an evolving hypersurface in motion within a scaled four-sphere universe.  I’ve noted that the measured cosmological constant is very close to $h^2$ before many times.  The evolution of $M_t$ may be completely dominated by electromagnetism and there would still be an evolution of $M_t$.  The resulting movement might bring regions of high curvature closer together and the effect would be gravitation.  This sort of purely geometric effect might explain why gravitation is so much weaker than electromagnetism as ‘classical forces’.