Conformal theory of gravitation and cosmology

Abstract

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. Conformal gravity (CG) has recently been fitted to rotation data for 138 galaxies. The conformal Higgs model (CHM) acquires a gravitational effect that fits observed Hubble expansion for redshifts $z\leq 1$ (7.33 Gyr) accurately with only one free constant parameter. The astrophysical data fitted by these two conformal models is shown here to account for both arbitrary parameters $w^2$ and $\lambda$ of postulated Higgs potential $V=-(w^2-\lambda\Phi^\dagger\Phi)\Phi^\dagger\Phi$, responsible for symmetry-breaking finite $\Phi^\dagger\Phi$ in electroweak particle theory. The present analysis resolves recent criticism of CG. CG and CHM are shown here to be interdependent but compatible. Nonclassical CG acceleration $\gamma$ is shown to be determined by the CHM. Conformal theory explains dark energy and does not require dark matter, a viable alternative to the $\Lambda$CDM standard model. A recently established empirical relationship between classical and nonclassical galactic radial acceleration requires parameter $\gamma$ to be independent of galactic mass. Conformal theory is shown here to be consistent with this and with the $v^4$ baryonic Tully-Fisher relation for galactic rotation velocities. Vanishing of centripetal acceleration outside a halo boundary is a unique implication of the theory.