The presence of a Phantom field in a Randall-Sundrum scenario

The presence of phantom dark energy in brane world cosmology generates important new effects, causing a premature Big Rip singularity when we increase the presence of extra dimension and considerably competing with the other components of our Universe. The idea is based first, in only considering a field with the characteristic equation $\omega<-1$ and after that, consider the explicit form of the scalar field with a potential with a maximum (with the aim of avoid a Big Rip singularity). In both cases we study the dynamic in a robust form through the dynamical analysis theory, detailing in parameters like the deceleration $q$ and the vector field associated to the dynamical system. Results are discussed with the purpose of deeming the cosmology with a phantom field as dark energy in a Randall-Sundrum scenario.