We study rapid-turn trajectories in a class of two-field cosmological models, whose scalar manifold is the Poincar 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 η-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 disk, unlike in the standard α-attractor case.

我们研究一类双场宇宙学模型中的快速转弯轨迹，其标量流形是庞加莱圆盘。多场暴涨的背景解决方案，场空间轨迹表现出急转弯，可以为原始黑洞 (PBH) 的形成埋下种子。我们研究了一类具有隐藏对称性的精确解，并表明它们表现出诱导 PBH 生成所需的瞬态快速转变周期。此外，我们放宽了对称条件，并在某个范围内找到了具有改进的哈勃 η 参数行为的修改解，这保留了所需的转向率函数形状。有趣的是，修改后的解决方案描述了一个短暂的超慢滚阶段，然后是长期慢滚充气。值得注意的是，慢滚发生在庞加莱圆盘的中心附近（而不是边界附近），