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, a sufficient amount of inflation and normalization to COBE requires a vacuum scale of 10¹⁶ GeV and a {φ} mass of 10¹³ GeV. Depending on the initial value of {φ}, our model can give either less ({~}n1) or more ({~}n>1) power on small scales compared to the scale-invariant spectrum (n=1), given the normalization to COBE. Given the same power on small scales, our power spectra can give more power on intermediate scales, compared to simple ``tilted'' power spectra.