On Primordial Black Holes from Rapid Turns in Two-field Models

TL;DR

This paper explores how rapid-turn trajectories in two-field inflation models with a Poincaré disk scalar manifold can lead to primordial black hole formation, presenting exact solutions and their implications for early universe cosmology.

Contribution

It introduces new exact solutions with hidden symmetry and modified solutions that exhibit rapid turns and ultra-slow roll phases, advancing understanding of PBH generation in multi-field inflation.

Findings

Transient rapid-turn periods can seed PBH formation.

Modified solutions improve the behavior of the Hubble η-parameter.

Slow roll inflation occurs near the disk center, unlike standard models.

Abstract

We study rapid-turn trajectories in a class of two-field cosmological models, whose scalar manifold is the Poincar\'e 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 Poincar\'e disk, unlike in the standard $\alpha$-attractor case.