We investigate general scalar field potentials V(phi) for inflationary
cosmology arising from spontaneous symmetry breaking. We find that po
tentials which are dominated by terms of order phi(m) with m > 2 can s
atisfy observational constraints at an arbitrary symmetry breaking sca
le. Of particular interest, the spectral index of density fluctuations
is shown to be independent of the specific form of the potential, dep
ending only on the order rn of the lowest non-vanishing derivative of
V(phi) near its maximum. The results of a model with a broken SO(3) sy
mmetry illustrate these features.