Weyl Current, Scale-Invariant Inflation and Planck Scale Generation

摘要

Scalar fields, $\phi_i$ can be coupled non-minimally to curvature and satisfythe general criteria: (i) the theory has no mass input parameters, includingthe Planck mass; (ii) the $\phi_i$ have arbitrary values and gradients, butundergo a general expansion and relaxation to constant values that satisfy anontrivial constraint, $K(\phi_i) =$ constant; (iii) this constraint breaksscale symmetry spontaneously, and the Planck mass is dynamically generated;(iv) there can be adequate inflation associated with slow roll in a scaleinvariant potential subject to the constraint; (v) the final vacuum can have asmall to vanishing cosmological constant (vi) large hierarchies in vacuumexpectation values can naturally form; (vii) there is a harmless dilaton whichnaturally eludes the usual constraints on massless scalars. These models aregoverned 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 invariantspecification of renormalized quantities.