标题： 在广义的$\mathcal{F}(H)$ 弗里德曼方程框架下重建膨胀和再加热 显示英文标题

标题： Reconstructing inflation and reheating in the framework of a generalized $\mathcal{F}(H)$ Friedmann equation

摘要： 考虑在修正的 Friedmann 方程框架下，将标量谱指数作为折叠数$e-$的参数化的膨胀宇宙重建问题被分析。 在此背景下，我们研究了在由$\mathcal{F}(H)\propto \rho$指定的修正 Friedmann 方程下，同时重建哈勃参数和有效势的可能性，其中$\mathcal{F}(H)$对应于哈勃参数$H$的任意函数，而$\rho$表示与宇宙中物质相关的能量密度。 为了在膨胀场景中重建背景变量，我们通过将谱指数表示为哈勃参数及其导数的函数，发展了一种新方法。 因此，我们利用慢滚近似以及将标量谱指数作为折叠数$e-$函数的参数化，得到了一种通用的膨胀重建形式化方法$N$。 作为具体例子，我们考虑最简单的吸引子$n_s-1=-2/N$以及与修正后的 Friedmann 方程相关的不同函数$\mathcal{F}(H)$，以重建以标量场$\phi$表示的哈勃参数和有效势。此外，我们通过考虑一个常数状态方程参数来研究重新加热阶段，在此期间，我们利用在不同$\mathcal{F}(H)-$模型重建过程中得到的背景变量来确定此阶段的温度和 e 折叠数。另外，我们使用来自普朗克和 BICEP/Keck 结果的当前天文数据，约束与重建的暴胀$\mathcal{F}(H)-$模型相关的不同参数，这些模型分别对应暴胀和重新加热阶段。 显示英文摘要

摘要： The reconstruction of an inflationary universe considering the parametrization of the scalar spectral index as a function of the number of $e-$folds in the framework of a modified Friedmann equation is analyzed. In this context, we examine the possibility of reconstructing the Hubble parameter together with the effective potential considering a modified Friedmann equation specified by $\mathcal{F}(H)\propto \rho$, where $\mathcal{F}(H)$ corresponds to an arbitrary function of the Hubble parameter $H$ and $\rho$ denotes the energy density associated with the matter in the universe. To reconstruct the background variables during the inflationary scenario, we develop a new methodology by expressing the spectral index in terms of the Hubble parameter and its derivatives. Thus, we obtain a general formalism for the reconstruction of the inflation, using the slow roll approximation together with the parametrization of the scalar spectral index as a function of the number of $e-$folds $N$. As specific examples, we consider the simplest attractor $n_s-1=-2/N$ together with different functions $\mathcal{F}(H)$, associated to the modified Friedmann equation, to rebuild the Hubble parameter and the effective potential in terms of the scalar field $\phi$. Additionally, we examine the reheating epoch by considering a constant equation of state parameter, in which we determine the temperature and the number of e-folds during this epoch, using the background variables found during the reconstruction of the different $\mathcal{F}(H)-$models studied. Besides, we constrain the different parameters associated with the reconstructed inflationary $\mathcal{F}(H)-$models during the epochs of inflation and reheating, using current astronomical data from Planck and BICEP/Keck results.