  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 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, are static
infinite planar domain walls separating vacua associated with different
spacetimes.
