Hilltop inflation

We study 'hilltop' inflation, in which inflation takes place near a maximum of the potential. Viewed as a model of inflation after the observable Universe leaves the horizon ( observable inflation), hilltop inflation is rather generic. If the potential steepens monotonically, observable hilltop inflation gives a tiny tensor fraction ( r less than or similar to 0.002). The usual F- and D-term models may easily be transmuted to hilltop models by Planck-suppressed terms, making them more natural. The only commonly considered model of observable inflation which is definitely not hilltop is tree-level hybrid inflation. Viewed instead as an initial condition, we explain that hilltop inflation is more generic than seems to have been previously recognized, adding thereby to the credibility of the idea that eternal inflation provides the pre-inflationary initial condition.