  Models of inflationary cosmology based on spontaneous symmetry breaking
typically suffer from the shortcoming that the symmetry breaking scale is
driven to nearly the Planck scale by observational constraints. In this paper
we investigate inflationary potentials in a general context, and show that this
difficulty is characteristic only of potentials $V(\phi)$ dominated near their
maxima by terms of order $\phi^2$. We find that potentials dominated by terms
of order $\phi^m$ with \hbox{$m > 2$} can satisfy observational constraints at
an arbitrary symmetry breaking scale. Of particular interest, the spectral
index of density fluctuations is shown to depend only on the order of the
lowest non-vanishing derivative of $V(\phi)$ near the maximum. This result is
illustrated in the context of a specific model, with a broken ${\rm SO(3)}$
symmetry, in which the potential is generated by gauge boson loops.
