# Hyperinflation generalised: from its attractor mechanism to its tension with the `swampland conjectures'

## TL;DR

This paper generalizes hyperinflation to multi-field models with broad potentials, analyzes its attractor mechanism, and discusses its compatibility with swampland conjectures and observational constraints.

## Contribution

It extends hyperinflation to models with multiple fields and non-symmetric potentials, providing a detailed proof of the attractor mechanism and explicit models.

## Key findings

- Hyperinflation can occur in multi-field, broad potential models.
- Models can satisfy some swampland conjectures but face tension with reheating.
- Generalizations can address issues with the weak gravity conjecture.

## Abstract

In negatively curved field spaces, inflation can be realised even in steep potentials. Hyperinflation invokes the `centrifugal force' of a field orbiting the hyperbolic plane to sustain inflation. We generalise hyperinflation by showing that it can be realised in models with any number of fields ($N_f\geq2$), and in broad classes of potentials that, in particular, don't need to be rotationally symmetric. For example, hyperinflation can follow a period of radial slow-roll inflation that undergoes geometric destabilisation, yet this inflationary phase is not identical to the recently proposed scenario of `side-tracked inflation'. We furthermore provide a detailed proof of the attractor mechanism of (the original and generalised) hyperinflation, and provide a novel set of characteristic, explicit models. We close by discussing the compatibility of hyperinflation with observations and the recently much discussed `swampland conjectures'. Observationally viable models can be realised that satisfy either the `de Sitter conjecture' ($V'/V\gtrsim 1$) or the `distance conjecture' ($\Delta \phi \lesssim 1$), but satisfying both simultaneously brings hyperinflation in some tension with successful reheating after inflation. However, hyperinflation can get much closer to satisfying all of these criteria than standard slow-roll inflation. Furthermore, while the original model is in stark tension with the weak gravity conjecture, generalisations can circumvent this issue.