Tuning the Cosmological Constant, Broken Scale Invariance, Unitarity

TL;DR

This paper investigates gravity with a cosmological constant and a scale-invariant sector, analyzing fluctuations around Minkowski space, and explores how breaking scale invariance affects the mass of metric perturbations and ghost freedom.

Contribution

It demonstrates how explicit breaking of scale invariance can cancel the mass term for metric trace perturbations, highlighting the role of Fierz-Pauli tuning and form fields.

Findings

Fierz-Pauli combination is ghost-free.

Explicit scale invariance breaking cancels the mass term.

Models with four-form fields mimic explicit symmetry breaking.

Abstract

We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the linearised level we find that the trace of metric perturbations receives a positive or negative mass squared contribution. However, only for the Fierz-Pauli combination the theory is free of ghosts. The mass term for the trace of metric perturbations can be cancelled by explicitly breaking scale invariance. This reintroduces fine-tuning. Models based on four form field strength show similarities with explicit scale symmetry breaking due to quantisation conditions.