  The scalar sector of the Randall-Sundrum model is discussed. The effective
potential for the Standard Model Higgs-boson (h) interacting with Kaluza-Klein
excitations of the graviton and the radion (phi) has been derived and it has
been shown that only the Standard Model-like vacuum is allowed. The theoretical
and experimental consequences of the curvature-scalar mixing xi RHH introduced
on the visible brane are considered and simple sum rules that relate the
couplings of the mass eigenstates (h) and (phi) to pairs of vector bosons and
fermions are derived. The sum rule for the ZZh and ZZ phi couplings in
combination with LEP/LEP2 data implies that not both the h and phi can be
light. We present explicit results for the still allowed region in the
(mh,mphi) plane that remains after imposing the LEP upper limits for
non-standard scalar couplings to a ZZ pair. The phenomenological consequences
of the mixing are investigated and, in particular, it is shown that the
Higgs-boson decay h -> phi phi would provide an experimental signature for
non-zero xi and can have a very substantial impact on the Higgs-boson searches,
having BR(h->phi phi) as large as 30 - 40 %.
