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