Inflation at low scales: General analysis and a detailed model

Models of inflationary cosmology based on spontaneous symmetry breaking typically suffer from the short-coming 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(φ) dominated near their maxima by terms of order φ². We find that potentials dominated by terms of order φ^m with 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 nonvanishing derivative V(φ) of near the maximum. This result is illustrated in the context of a specific model, with a broken SO(3) symmetry, in which the potential is generated by gauge boson loops.