Self-tuning and the derivation of the Fab Four

TL;DR

This paper rigorously derives the Fab Four scalar-tensor theories from Horndeski's general model, establishing them as the unique classical solutions capable of addressing the cosmological constant problem through self-tuning.

Contribution

It proves that the Fab Four are the only classical scalar-tensor theories within Horndeski's framework that can potentially solve the cosmological constant problem.

Findings

Derivation of the Fab Four from Horndeski's theory.

Full equations of motion for the Fab Four.

Heuristic argument for controlling radiative corrections.

Abstract

We have recently proposed a special class of scalar tensor theories known as the Fab Four. These arose from attempts to analyse the cosmological constant problem within the context of Horndeski's most general scalar tensor theory. The Fab Four together give rise to a model of self-tuning, with the relevant solutions evading Weinberg's no-go theorem by relaxing the condition of Poincare invariance in the scalar sector. The Fab Four are made up of four geometric terms in the action with each term containing a free potential function of the scalar field. In this paper we rigorously derive this model from the general model of Horndeski, proving that the Fab Four represents the only classical scalar tensor theory of this type that has any hope of tackling the cosmological constant problem. We present the full equations of motion for this theory, and give an heuristic argument to suggest that one might be able to keep radiative corrections under control. We also give the Fab Four in terms of the potentials presented in Deffayet et al's version of Horndeski.