  Recently, Pani, Sotiriou, and Vernieri explored a new theory of gravity by
adding nondynamical fields, i.e., gravity with auxiliary fields [Phys. Rev. D
88, 121502(R) (2013)]. In this gravity theory, higher-order derivatives of
matter fields generically appear in the field equations. In this paper we
extend this theory to any dimensions and discuss the thick braneworld model in
five dimensions. Domain wall solutions are obtained numerically. The stability
of the brane system under the tensor perturbation is analyzed. We find that the
system is stable under the tensor perturbation and the gravity zero mode is
localized on the brane. Therefore, the four-dimensional Newtonian potential can
be realized on the brane.
