Fermilab Cosmic Physics Center

Scalar fields can be coupled non-minimally to curvature and satisfy: (i) the theory has no mass input parameters, including M_Planck=0; (ii) the scalars have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial elliptical constraint K(phi)=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 VEV’s can naturally form; (vii) there is a harmless dilation which naturally eludes the usual constraint on massless scalars. These models are governed by a global Weyl scale symmetry and its conserved current, K_mu. At the quantum level of the Weyl scale symmetry can be maintained by an invariant specification of renormalization.