Evolving Planck Mass in Classically Scale-Invariant Theories

TL;DR

This paper explores how classically scale-invariant theories with scalar fields can dynamically generate the Planck mass, analyze their stability under explicit scale-breaking sources, and discuss implications for cosmology and dark matter.

Contribution

It demonstrates that quantum corrections can stabilize the fixed point in these theories and shows that current cosmological constraints do not significantly limit their parameters.

Findings

Quantum corrections stabilize the fixed point near the Coleman-Weinberg minimum.

Cosmological constraints from Big Bang Nucleosynthesis are weak for these models.

Oscillations around the fixed point could contribute to dark matter density.

Abstract

We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.