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

Understand

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 Poincar\'e 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.