Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

Understand

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold.

• We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation.
• We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit.
• In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation.