In this paper we present a new cosmological inflationary model which is constructed using the Ivanov-Salopek-Bond method with a logistic generating function. We derive the inflationary observables as well as the duration and temperature of the subsequent reheating epoch of our model exactly, with no need to recur to the slow roll approximation. The obtained scalar spectral index and tensor-to-scalar ratio of perturbations fall comfortably within the range of the measurements presented by the Planck collaboration. On the other hand, for the reheating era, our model predicts a relatively small number of e-folds and thus high temperatures, still within range of Planck’s bounds. We then consider a generalization of our model that we refer to as Bernoulli-like functions and examine different scenarios that are encompassed within this generalization.

在本文中，我们提出了一种新的宇宙学通货膨胀模型，该模型是使用具有逻辑生成函数的伊万诺夫-萨洛普克-邦德方法构造的。我们可以精确得出通货膨胀的可观测值以及模型的后续再加热时期的持续时间和温度，而无需重复进行慢滚动近似。所获得的标量谱指数和扰动的张量/标量比在Planck合作提供的测量范围内是合适的。另一方面，对于再热时代，我们的模型预测相对较少的电子折叠，从而预测高温，仍在普朗克的范围内。然后，我们考虑模型的一般化，我们将其称为类伯努利函数，并研究该一般化所包含的不同场景。