General second order scalar-tensor theory, self tuning, and the Fab Four

TL;DR

The paper identifies the Fab Four as the unique self-tuning subset of Horndeski's general scalar-tensor theory capable of screening the net cosmological constant on FLRW backgrounds while maintaining nontrivial cosmology. By analyzing phase-transition robustness and enforcing a self-tuning filter, the authors show that the Horndeski action reducing to four base Lagrangians with scalar-dependent potentials is necessary to evade Weinberg's no-go theorem. The resulting Fab Four—John, Paul, George, and Ringo—together with a bare cosmological term, define a cosmology in which vacuum energy is dynamically screened but still allows evolution, with John and Paul providing key derivative interactions to enable screening mechanisms. The work highlights deep geometric connections (Euler densities) and outlines important phenomenological and quantum-stability questions for future study.

Abstract

Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.