Conformal theory of gravitation and cosmic expansion

The postulate of universal Weyl conformal symmetry for all elementary physical fields introduces nonclassical gravitational effects in both conformal gravitation(CG) and the conformal Higgs model (CHM). The resulting theory is found to explain major observed phenomena including excessive galactic rotation velocities and accelerating Hubble expansion, without invoking dark matter (DM). The recent history of this development is surveyed here. Implications of the theory include galactic baryonic Tully-Fisher relations and dark galactic haloes of definite large radius. Cosmological CHM parameters exclude a massive Higgs boson but are consistent with a novel alternative particle of the observed mass.