Dimensional Transmutation in Gravity and Cosmology

TL;DR

This paper explores theories where all mass scales arise from dimensional transmutation, emphasizing quantum consistency, UV completion, and phenomenological implications like horizonless compact objects and observable signatures in cosmology and gravitational waves.

Contribution

It extends the analysis of scale-invariant gravity theories with four-derivative actions, demonstrating unitarity, stability, and potential observational tests.

Findings

Four-derivative gravity terms enable UV complete models.

Horizonless ultracompact objects replace small black holes.

Predictions align with CMB observations and GW detection prospects.

Abstract

We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four derivatives of the metric. It is shown, nevertheless, how unitary is achieved and the classical Ostrogradsky instabilities can be avoided. The four-derivative terms also allow us to have a UV complete framework and a naturally small ratio between the Higgs mass and the Planck scale. Moreover, black holes of Einstein gravity with horizons smaller than a certain (microscopic) scale are replaced by horizonless ultracompact objects that are free from any singularity and have interesting phenomenological applications. We also discuss the predictions that can be compared with observations of the microwave background radiation anisotropies and find that this scenario is viable and can be tested with future data. Finally, how strong phase transitions can emerge in models of this type with approximate scale symmetry and how to test them with GW detectors is reviewed and explained.