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Starting from the most general scalar-tensor theory with second order fieldequations in four dimensions, we establish the unique action that will allowfor the existence of a consistent self-tuning mechanism on FLRW backgrounds,and show how it can be understood as a combination of just four baseLagrangians with an intriguing geometric structure dependent on the Ricciscalar, the Einstein tensor, the double dual of the Riemann tensor and theGauss-Bonnet combination. Spacetime curvature can be screened from the netcosmological constant at any given moment because we allow the scalar field tobreak Poincar\'e invariance on the self-tuning vacua, thereby evading theWeinberg no-go theorem. We show how the four arbitrary functions of the scalarfield combine in an elegant way opening up the possibility of obtainingnon-trivial cosmological solutions.

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