In this paper we consider a geometrical Yukawa coupling as a solution to the problem of gauge field localization. We show that upon dimensional reduction the vector field component of the field is localized but the scalar component (A5) is not. We show this for any smooth version of the Randall–Sundrum model. The covariant version of the model with geometrical coupling simplifies the generalization to smooth versions generated by topological defects. This kind of model has been considered some time ago, but there it has been introduced with two free parameters in order to get a localized solution which satisfy the boundary conditions: a mass term in five dimensions and a coupling with the brane. The boundary condition fixes one of them and the model is left with one free parameter M. First we show that by considering a Yukawa coupling with the Ricci scalar it is possible to unify these two parameters into just one fixed by the boundary condition. With this we get a consistent model with no free parameters and the mass term can be interpreted as a coupling to the cosmological constant

Two different solutions to the problem of the zero-mode localization of the Elko spinor are presented. The first solution is given by the introduction of a mass term and by coupling the spinor with the brane through a delta function. The second solution is reached by a Yukawa geometrical coupling with the Ricci scalar. These two models consistently change the boundary condition at infinity and at the origin. For the case of the geometrical coupling, we are able to show that the zero mode is localized for any smooth version of the Randall-Sundrum model.

In this manuscript we show that the geometrical localization mechanism implies a four dimensional mass for the photon. The consistence of the model provides a mass given exactly by mγ=R/4 where R is the Ricci scalar. As a consequence, the cosmological photon has a mass related to the vacuum solution of the Einstein equation. At the present age of the universe we have a dS vacuum with R=4Λ, where Lambda is a positive cosmological constant. With this we find that mγ≈2×10−69 kg, which is below the present experimental upper bounds, and such correction may be observed in the next years with more precise measurements. By considering the value of R inside some astrophysical sources and environments we find that the bound is also satisfied. The experimental verification of this mass, beyond pointing to the existence of extra dimensions, would imply in a fundamental change in cosmology, astrophysics and in particle physics