On primordial black holes from rapid turns in two-field models

We study rapid-turn trajectories in a class of two-field cosmological models, whose scalar manifold is the Poincare disk. Background solutions in multi-field inflation, with field-space trajectories exhibiting sharp turns, can seed primordial black hole (PBH) formation. We investigate a class of exact solutions with hidden symmetry and show that they exhibit the kind of transient rapid-turn period, needed to induce PBH generation. Furthermore, we relax the symmetry condition and find, in a certain regime, modified solutions with improved behavior of the Hubble eta-parameter, which preserve the desired shape of the turning rate function. Interestingly, the modified solutions describe a brief ultra-slow roll phase, followed by long-term slow roll inflation. It is notable that slow roll occurs near the center (not near the boundary) of the Poincare disk, unlike in the standard alpha-attractor case.

Automated summary

In this study, rapid-turn trajectories in a class of two-field cosmological models are investigated, showing that certain solutions can induce primordial black hole formation through a transient rapid-turn period. By relaxing the symmetry condition, modified solutions were found with improved behavior of the Hubble eta-parameter, including a brief ultra-slow roll phase followed by long-term slow roll inflation. Slow roll was observed near the center of the Poincare disk, in contrast to the standard alpha-attractor case.