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 dimensions and considerably competing with the other components of our Universe. This article first considers only a field with the characteristic equation $\omega <-1$ and then the explicit form of the scalar field with a potential with a maximum (with the aim of avoiding a big rip singularity). In both cases we study the dynamics robustly through dynamical analysis theory, considering in detail parameters such as the deceleration q and the vector field associated to the dynamical system. Results are discussed with the purpose of treating the cosmology with a phantom field as dark energy in a Randall–Sundrum scenario. (paper)