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 (∼n<1) 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