Cosmology and the Fate of Dilatation Symmetry

TL;DR

The paper investigates how dilatation symmetry and its quantum anomaly affect the cosmological constant problem. It argues that if dilatation symmetry is anomaly-free, a nontrivial minimum of the scale-free potential can yield realistic cosmology with a vanishing effective CC; when a dilatation anomaly is present, a cosmon field driven by the anomaly can dynamically suppress the cosmological constant and potentially lead to time-varying gravity and a light long-range force. The analysis connects short-distance renormalization-group behavior to large-scale cosmology, proposing an anomalous RG equation for the cosmological constant and exploring cosmologies where the CC evolves with time. Depending on the relative size of the intrinsic scale m and the sliding scale χ, several observationally distinct scenarios emerge, including late-time CC relaxation and possible deviations from standard Big Bang cosmology. This framework offers a dynamical route to the small observed CC and links cosmology to the ultraviolet structure of the fundamental theory.

Abstract

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a non-trivial minimum. For theories with dilatation anomaly one needs as a non-trivial "cosmon condition" that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.