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 $ϕ$. 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 $V(ϕ)$. In the examples studied here, sufficient amount of inflation and normalization to COBE require a vacuum scale of $10^{16}$ GeV and a $ϕ$ mass of $10^{13}$ GeV. Depending on the initial value of $ϕ$, our model can give either less ($\sim n<1$) or more ($\sim n>1$) power on small scales compared to the scale-invariant spectrum ($n=1$), given the normalization to COBE.
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