  We investigate quantum fluctuations on a de Sitter (dS) brane, which has its
own thickness, in order to examine whether or not the finite thickness of the
brane can act as a natural cut-off for the Kaluza-Klein (KK) spectrum. We
calculate the amplitude of the KK modes and the bound state by using the zeta
function method after a dimensional reduction.We show that the KK amplitude is
finite for a given brane thickness and in the thin wall limit the standard
surface divergent behavior is recovered. The strength of the divergence in the
thin wall limit depends on the number of dimensions, e.g., logarithmic on a two
dimensional brane and quadratic on a four dimensional brane. We also find that
the amplitude of the bound state mode and KK modes depends on the choice of
renormalization scale; and for fixed renormalization scales the bound state
mode is insensitive to the brane thickness both for two and four-dimensional dS
branes.

High Energy Physics - Theory;Astrophysics;General Relativity and Quantum Cosmology