This manuscript explores the dynamics of an inflationary model using two known exact solutions, i.e. , logamediate and exponential expansion. To achieve this, the framework of generalized induced gravity non-minimally coupled to Ricci scalar is taken under consideration. Using slow-roll approximation and a generalized form of coupling function, we find the possible forms of potential needed to produce inflation in the model and conduct the mathematical analysis of cosmological perturbations. In both of the eras, we constraint the involved model parameters by comparing the r − n s $r-n_{s}$ trajectories with Planck 2015 astrophysical data. Also, we reconstruct these inflationary models assuming as attractors the scalar spectral index and tensor-scalar ratio as a function of number of e-foldings.

中文翻译：

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使用广义诱导重力情景重建对数和指数膨胀模型

这份手稿使用两个已知的精确解，即对数展开和指数展开来探索膨胀模型的动力学。为了实现这一点，考虑了非最小耦合到 Ricci 标量的广义诱导重力框架。使用慢滚近似和耦合函数的广义形式，我们找到了在模型中产生膨胀所需的可能形式，并对宇宙学扰动进行数学分析。在这两个时代，我们通过将 r − ns $r-n_{s}$ 轨迹与 Planck 2015 天体物理数据进行比较来约束所涉及的模型参数。此外，我们重建这些膨胀模型，假设作为吸引子的标量谱指数和张量 - 标量比作为 e 折叠数量的函数。