In this paper, we investigate the effects of Type IV singularity through [Formula: see text] gravity description of inflationary Universe, where [Formula: see text] denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a [Formula: see text] model according to a given Hubble rate susceptible to describe the inflationary era near the Type IV singularity. One obtains an interesting well-known [Formula: see text] model but with additional constant parameter [Formula: see text] staying as the Type IV singularity contribution. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV singularity, indicating that a dynamical instability of the cosmological system occurs at that point. This means that the dynamical cosmological evolution up to that point ceases to be the final attractor since the system is abruptly interrupted. Furthermore, by considering the [Formula: see text] trace anomaly equation, the previous result on the Type IV singularity is consolidated by the conditional instability coming from the de Sitter inflationary description of the reconstructed [Formula: see text] model. The model leads to instability strongly governed by the Type IV singularity parameter [Formula: see text] is viewed as the graceful exit from inflation. Our theoretical [Formula: see text] description based on slow-roll parameters not only confirms some observational data on spectral index and the scalar-to-tensor ratio from Planck data and BICEP[Formula: see text]/Keck-Array data, but also shows the property of [Formula: see text] gravity in describing the early and late-time evolution of our Universe.

中文翻译：

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围绕 f(T) 引力范围内 IV 型奇点的宇宙膨胀研究

在本文中，我们通过[公式：见文本]对暴胀宇宙的引力描述来研究IV型奇点的影响，其中[公式：见文本]表示扭转标量。利用该理论的弗里德曼方程，我们根据给定的哈勃率重构了一个[公式：见正文]模型，该模型易于描述IV型奇点附近的暴胀时代。一个人获得了一个有趣的众所周知的 [公式：见文本] 模型，但附加的常数参数 [公式：见文本] 保持为 IV 型奇点贡献。此外，我们计算哈勃流参数以确定宇宙系统的动态演化。结果表明，一些哈勃流参数在IV型奇点附近很小，在IV型奇点处变得奇异，表明宇宙系统的动态不稳定性发生在这一点上。这意味着由于系统突然中断，到那时为止的动态宇宙学演化不再是最终的吸引子。此外，通过考虑 [公式：见文本] 迹异常方程，先前关于 IV 型奇点的结果被来自重构的 [公式：见文本] 模型的德西特暴胀描述的条件不稳定性巩固。该模型导致受第四类奇点参数[公式：见文本]强烈控制的不稳定性，被视为暴胀的优雅退出。我们的理论[公式：