Self-tuning and the derivation of the Fab Four
Christos Charmousis, Edmund J. Copeland, Antonio Padilla, Paul M. Saffin
TL;DR
This work reframes the cosmological constant problem within Horndeski gravity and advocates a self-tuning approach that allows the scalar sector to break Poincaré invariance while keeping curvature compatible with a Minkowski vacuum for arbitrary vacuum energy $\rho_\Lambda$. Through a three-part self-tuning filter, the authors show that the Fab Four—John, Paul, George, and Ringo—are the unique classical scalar-tensor sector in this class capable of absorbing vacuum energy and sustaining nontrivial cosmology, with each term corresponding to a geometric contraction of curvature and scalar derivatives. The Fab Four arise from a reduction of the Horndeski action to four $\phi$-dependent potentials, are equivalent (up to total derivatives) to Deffayet et al.'s generalized galileon form, and possess second-order equations of motion and a Lovelock-type geometric origin. The paper discusses phenomenological prospects (e.g., Vainshtein screening), the role of radiative corrections, and outlines future work on cosmological solutions, solar-system tests, and stability analyses, framing a concrete yet challenging route toward addressing the cosmological constant problem.
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.