  We construct explicitly deformations of Einstein's theory of gravity that are
consistent and phenomenologically viable since they respect, in particular,
cosmological backgrounds. We show that these deformations have unique
symmetries in accordance with unitarity requirements, and give rise to a
curvature induced self-stabilizing mechanism. As a consequence, any nonlinear
completed deformation must incorporate self-stabilization on generic spacetimes
already at lowest order in perturbation theory. Furthermore, our findings
include the possibility of consistent and phenomenologically viable
deformations of general relativity that are solely operative on curved
spacetime geometries, reducing to Einstein's theory on the Minkowski
background.
