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This is the second of three papers on Conformal General Relativity (CGR). Theconformal group is introduced here as the invariance group of the partial orderof causal events in $n$D spacetime. Its general structure, discrete symmetriesand field representations are described in detail. The spontaneous breakdown ofconformal symmetry is then discussed and the role played by a ghost scalarfield and a physical scalar field in 4D spacetime are evidenced. Kinematic--,conformal-- and proper--time hyperbolic coordinates are introduced in anegatively curved Milne spacetime for the purpose of providing three differentbut equivalent representations of CGR. The first of these is grounded in aRiemannian manifold and is manifestly conformal invariant, the second isgrounded in a conformally connected Cartan manifold but its conformalinvariance is hidden, the third is grounded in the Riemannian manifold of theMilne spacetime and has the formal structure of General Relativity (GR). Therelation between CGR and standard inflationary cosmology is also brieflydiscussed. Lastly, in view of the detailed study of Higgs--field dynamicscarried out in the third paper, the action integrals, motion equations andtotal energy--momentum tensors of the Higgs field interacting with the dilationfield are described in the three representations mentioned above.

The Conformal Universe II: Conformal Symmetry, its Spontaneous Breakdown and Higgs Fields in Conformally Flat Spacetime