Using the probe brane construction of higher derivative effective field theories, extended to higher co-dimensions and curved spaces, we construct galileon and DBI theories on de Sitter space with N fields and an \( \mathfrak{so}(N) \) internal symmetry, non-linearly realizing the symmetries of a higher dimensional de Sitter space. In some cases, the theory admits a non-trivial vacuum that spontaneously breaks the \( \mathfrak{so}(N) \) symmetry, and around this vacuum the Goldstone modes have vanishing kinetic terms and become infinitely strongly coupled. This gives an example of a scalar effective field theory with two de Sitter vacua, one of which appears to have Boulware-Deser-like ghosts, and one of which does not.
