Tuning the cosmological constant, broken scale invariance, unitarity

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.

Superfluids and the cosmological constant problem

“…In this sense, the positivity of a is a requirement imposed on any sensible UV completion of our model, much along the lines of other such positivity bounds in effective field theories[70] 25. Such a theory was considered by ref [71]. in the context of the cosmological constant problem.…”