The Conformal Universe I: Physical and Mathematical Basis of Conformal General Relativity

Abstract

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 $σ(x)$ invested with geometric meaning and a physical scalar field $φ(x)$ of zero mass, both of which have nonzero vacuum expectation values; 3) in order to preserve $S$--matrix unitarity, $σ(x)$ and $φ(x)$ must interact in such a way that the total energy density is bounded from below; 4) this interaction makes $φ(x)$ 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.