  We investigate scalar perturbations from inflation in braneworld cosmologies
with extra dimensions. For this we calculate scalar metric fluctuations around
five dimensional warped geometry with four dimensional de Sitter slices. The
background metric is determined self-consistently by the (arbitrary) bulk
scalar field potential, supplemented by the boundary conditions at both
orbifold branes. Assuming that the inflating branes are stabilized (by the
brane scalar field potentials), we estimate the lowest eigenvalue of the scalar
fluctuations - the radion mass. In the limit of flat branes, we reproduce well
known estimates of the positive radion mass for stabilized branes.
Surprisingly, however, we found that for de Sitter (inflating) branes the
square of the radion mass is typically negative, which leads to a strong
tachyonic instability. Thus, parameters of stabilized inflating braneworlds
must be constrained to avoid this tachyonic instability. Instability of
"stabilized" de Sitter branes is confirmed by the BraneCode numerical
calculations in the accompanying paper hep-th/0309001. If the model's
parameters are such that the radion mass is smaller than the Hubble parameter,
we encounter a new mechanism of generation of primordial scalar fluctuations,
which have a scale free spectrum and acceptable amplitude.
