Weyl Current, Scale-Invariant Inflation and Planck Scale Generation

TL;DR

This paper explores a class of scale-invariant scalar field models coupled to gravity, demonstrating how they can generate the Planck scale dynamically, support inflation, and naturally produce hierarchies without explicit mass parameters.

Contribution

It introduces a framework where Weyl scale symmetry governs scalar-curvature couplings, enabling spontaneous symmetry breaking and Planck scale generation without explicit mass terms.

Findings

Planck scale generated dynamically through spontaneous symmetry breaking.

Models support slow-roll inflation within scale-invariant potentials.

Dilaton remains harmless and evades constraints on massless scalars.

Abstract

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.