Dynamics of a self-interacting scalar field trapped in the braneworld for a wide variety of self-interaction potentials

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped in the braneworld, for a wide variety of self-interaction potentials. We focus on Randall-Sundrum and on Dvali-Gabadadze-Porrati braneworld models exclusively. These models are complementary to each other: while the Randall-Sundrum brane produces UV) corrections to general relativity, the Dvali-Gabadadze-Porrati braneworld modifies Einstein's theory at large scales, i e., produces IR modifications of general relativity. This study of the asymptotic properties of both braneworld models, shows - in the phase space - the way the dynamics of a scalar field trapped in the brane departs from standard general relativity behavior.