  This is the first of three papers on Conformal General Relativity (CGR),
which differs from Einstein's General Relativity (GR) in that it requires
action--integral invariance under local scale transformations in addition to
general coordinate transformations. The theory is here introduced in the
semiclassical approximation as a preliminary approach to a quantum theoretical
implementation. The idea of a conformal--invariant extension of GR was
introduced by Weyl in 1919. For several decades it had little impact, as CGR
implies that all fields are massless. Today this does not appear to be an
unsurmountable difficulty since nonzero mass parameters may result from the
spontaneous breakdown of conformal symmetry. The theory leads to very
interesting results and predictions: 1) the spontaneous breakdown of conformal
symmetry is only possible in a 4D--spacetime with small negative curvature; 2)
CGR requires the introduction of a ghost scalar field $\sigma(x)$ invested with
geometric meaning and a physical scalar field $\varphi(x)$ of zero mass, both
of which have nonzero vacuum expectation values; 3) in order to preserve
$S$--matrix unitarity, $\sigma(x)$ and $\varphi(x)$ must interact in such a way
that the total energy density is bounded from below; 4) this interaction makes
$\varphi(x)$ behave like a Higgs field of varying mass, which is capable of
promoting a huge energy transfer from geometry to matter identifiable as the
big bang; 5) in the course of time, the Higgs boson mass becomes a constant and
CGR converges to GR.
