Inflation From Symmetry Breaking Below the Planck Scale

Abstract

We investigate general scalar field potentials \hbox{$V\left(ϕ\right)$} for inflationary cosmology arising from spontaneous symmetry breaking. We find that potentials which are dominated by terms of order $ϕ^m$ 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 be independent of the specific form of the potential, depending only on the order $m$ of the lowest non-vanishing derivative of $V(ϕ)$ near its maximum. The results of a model with a broken ${\rm SO(3)}$ symmetry illustrate these features.