The effective inflationary Lagrangian is a prominent challenge for theoretical cosmologists, since it may contain imprints of the quantum epoch. In view of the fact that higher order curvature terms might be present in the effective inflationary Lagrangian, in this work we introduce the theoretical framework of power-law $f\left(R\right)$ gravity corrected canonical scalar field inflation, aiming to study the inflationary dynamics of this new framework. The main characteristic of this new theoretical framework is the dominance of a power-law $f\left(R\right)$ gravity term $\sim R^n$, with $1<n<2$, compared to the Einstein–Hilbert term $\sim R$. In effect, the field equations are controlled by the $R^n$ term in contrast to the Einstein–Hilbert canonical scalar theory. We extract the slow-roll field equations and we calculate the slow-roll indices of the resulting theory which acquire quite elegant final form, when the slow-roll conditions hold true. Accordingly, we examine quantitatively the inflationary phenomenological implications of the theoretical framework we introduced, by choosing simple hybrid-like scalar field potentials. As we evince the resulting theory is in good agreement with the latest Planck data for a wide range of the free parameters of the model. Thus our theoretical framework makes possible to obtain viable inflationary theories, which otherwise would be non-viable, such as the simple power-law $f\left(R\right)$ gravity model or the simple power-law scalar model.

有效的暴胀拉格朗日对理论宇宙学家来说是一个突出的挑战，因为它可能包含量子时代的印记。鉴于有效膨胀拉格朗日函数中可能存在高阶曲率项，本文引入幂律理论框架$F\left(\mathrm{电阻}\right)$重力校正规范标量场膨胀，旨在研究这个新框架的膨胀动力学。这种新理论框架的主要特征是幂律的支配地位$F\left(\mathrm{电阻}\right)$ 重力项 $～{\mathrm{电阻}}^n$， 和 $1<n<2$, 与爱因斯坦-希尔伯特项相比 $～\mathrm{电阻}$. 实际上，场方程由${\mathrm{电阻}}^n$与爱因斯坦-希尔伯特规范标量理论相反的术语。我们提取慢滚场方程并计算所得理论的慢滚指数，当慢滚条件成立时，该指数获得非常优雅的最终形式。因此，我们通过选择简单的类似混合的标量场势，定量地研究了我们引入的理论框架的膨胀现象学含义。正如我们所证明的那样，对于模型的各种自由参数，所得理论与最新的普朗克数据非常吻合。因此，我们的理论框架使得获得可行的膨胀理论成为可能，否则这些理论是不可行的，例如简单的幂律$F\left(\mathrm{电阻}\right)$ 重力模型或简单的幂律标量模型。