Horizon-Flow off-track for Inflation

Inflation can be parameterized by means of truncated flow equations. In this "horizon-flow" setup, generic results have been obtained, such as typical values for $r/(1-n_\mathrm{S})$. They are sometimes referred to as intrinsic features of inflation itself. In this paper we first show that the phenomenological class of inflationary potentials sampled by horizon-flow is directly responsible for such predictions. They are therefore anything but generic. Furthermore, the horizon-flow setup is shown to rely on trajectories in phase space that differ from the slow-roll. For a given potential, we demonstrate that this renders horizon-flow blind to entire relevant inflationary regimes, for which the horizon-flow trajectory is shown to be unstable. This makes horizon-flow a biased parameterization of inflation.