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 $V(\ensuremath{\varphi})$ dominated near their maxima by terms of order ${\ensuremath{\varphi}}^{2}$. We find that potentials dominated by terms of order ${\ensuremath{\varphi}}^{m}$ 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 of $V(\ensuremath{\varphi})$ 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.

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