  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.
