Weyl Current, Scale-Invariant Inflation and Planck Scale Generation
  Scalar fields, $\phi_i$ can be coupled non-minimally to curvature and satisfy
the general criteria: (i) the theory has no mass input parameters, including
the Planck mass; (ii) the $\phi_i$ have arbitrary values and gradients, but
undergo a general expansion and relaxation to constant values that satisfy a
nontrivial constraint, $K(\phi_i) =$ constant; (iii) this constraint breaks
scale symmetry spontaneously, and the Planck mass is dynamically generated;
(iv) there can be adequate inflation associated with slow roll in a scale
invariant potential subject to the constraint; (v) the final vacuum can have a
small to vanishing cosmological constant (vi) large hierarchies in vacuum
expectation values can naturally form; (vii) there is a harmless dilaton which
naturally eludes the usual constraints on massless scalars. These models are
governed by a global Weyl scale symmetry and its conserved current, $K_\mu$ .
At the quantum level the Weyl scale symmetry can be maintained by an invariant
specification of renormalized quantities.
