Weyl Current, Scale-Invariant Inflation and Planck Scale Generation

Abstract

Scalar fields, ${\varphi }_i$ 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 ${\varphi }_i$ have arbitrary values and gradients, but undergo a general expansion and relaxation to constant values that satisfy a nontrivial constraint, $K({\varphi }_i)=$ 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.

17 pages, 3 figures; v2, fixed typos, and improved Section V

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• Inflation with Massive Spin-2 Ghosts
• Quantization of time and the big bang via scale-invariant loop gravity
• Higgs-Dilaton Inflation in Einstein-Cartan gravity
• Quintessence in Multi-Measure Generalized Gravity Stabilized by Gauss-Bonnet/Inflaton Coupling