Title: Hyperinflation,
Abstract: A model of cosmological inflation is proposed in which field space is a
hyperbolic plane. The inflaton never slow-rolls, and instead orbits the bottom
of the potential, buoyed by a centrifugal force. Though initial velocities
redshift away during inflation, in negatively curved spaces angular momentum
naturally starts exponentially large and remains relevant throughout. Quantum
fluctuations produce perturbations that are adiabatic and approximately scale
invariant; strikingly, in a certain parameter regime the perturbations can grow
double-exponentially during horizon crossing.