The Horndeski gravity yields domain wall solutions that connect asymmetric vacua for a certain region of parameters.In the thin wall limit there exist BPS domain walls that connect laubade 1973 stable vacua.That is, the false vacua in this theory follows the same effect obtained in supergravity vacua, i.e., it does not decay according to Coleman-de Luccia theory and the BPS solutions interpolating different vacua, e.
g., non-degenerate AdS vacua, sharps honda are static infinite planar domain walls separating vacua associated with different spacetimes.