No-go theorems in cubic sector of shift-symmetric Horndeski gravity
Horndeski gravity is a promising alternative gravity candidate because the size of its parameter space is sufficiently large to allow fine tuning of the cosmological constant and screening of the scalar field at solar system scales. The advantage of having a large parameter space, however, comes with the difficulty of searching for solutions and no-hair and no-go theorems become very helpful tools in overcoming this obstacle. Restricting our attention to the static and spherically-symmetric scalar and tensor fields, we prove no-go theorems in the cubic sector of shift-symmetric Horndeski gravity, G2 = X + L and G3 = P/XQ, where L, P, Q are constants and X is the kinetic term. We show that a nontrivial scalar field cannot live in a flat background with no vacuum energy and a Schwarzschild-de Sitter-like background.