Polynomial Hybrid Inflation

We study a simple extension of Linde’s hybrid inflation model, with the inflaton mass term replaced by the most general renormalizable potential for $\varphi$. The unprocessed power spectrum of density perturbations can have two minima and one maximum, roughly corresponding to two steep regions separated by a somewhat flat region in $V(\varphi )$. In the examples studied here, sufficient amount of inflation and normalization to COBE require a vacuum scale of ${10}^{16}$ GeV and a $\varphi$ mass of ${10}^{13}$ GeV. Depending on the initial value of $\varphi$, our model can give either less ($\sim n<1$) or more ($\sim n>1$)poweronsmallscalescomparedtothescale-invariantspectrum($n=1$), given the normalization to COBE.