From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.

中文翻译：

---

洛伦兹典型通货膨胀

假设慢滚参数[公式：见正文]具有作为 e 折叠数 [公式：见正文]的函数的洛伦兹形式，就获得了典型暴胀的成功模型。该形式对应于暴胀和暗能量时期的真空能量。该形式满足在暴胀时期结束时从[公式：见文本]的小值攀升到[公式：见文本]的条件。在宇宙晚期，[公式：见正文]再次变小，这导致了暗能量时代。模型预测的可观察值与最新的普朗克数据相符：[公式：见正文]。自然地，一个巨大的无量纲因子指数放大了暴胀尺度，指数抑制了暗能量尺度的出现，产生了一种宇宙学跷跷板机制。