# Hyperinflation

## TL;DR

This paper introduces a novel cosmological inflation model where the inflaton moves in a hyperbolic field space, leading to unique dynamics and potentially exponential growth of perturbations, differing from traditional slow-roll models.

## Contribution

It presents a new inflationary framework with hyperbolic field space where the inflaton orbits the potential bottom, maintaining angular momentum and producing distinctive quantum fluctuations.

## Key findings

- Perturbations are adiabatic and nearly scale-invariant.
- In certain regimes, perturbations grow double-exponentially during horizon crossing.
- The model challenges traditional slow-roll inflation assumptions.

## 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.