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

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 ($N_fgeq2$), and in broad classes of potentials that, in particular, dont 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 ($V/Vgtrsim 1$) 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.