The reconstruction of a k-essence inflationary universe, considering the unification between the swampland criteria and the attractor given by the scalar spectral index $n_S(N)$ together with the slow roll parameter $\epsilon(N)$in terms of the number of $e$-folds $N$ is studied. In the context of a coupling of the form $L(\phi)\,X$ in the k-essence model, we find the effective potential $V$ and the coupling parameter $L$ in terms of the scalar spectral index and the slow roll parameter under a general formalism. To apply the unification in our model, we consider some examples in order to rebuild the effective potential $V(\phi)$ and the coupling parameter $L(\phi)$ as a function of the inflaton field $\phi$. Here, we find that the reconstruction gives rise to an exponential potential and also to natural and hyperbolic inflation, respectively. Thus, in this article we show that it is possible to unify the theoretical foundations from the swampland criteria and the observational parameters corroborated by observations, in the reconstruction of an inflationary universe.

中文翻译：

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重构k-essence：统一吸引子nS(N)和沼泽标准

k-本质暴胀宇宙的重建，考虑沼泽地标准和由标量光谱指数$n_S(N)$以及慢滚参数$\epsilon(N)$给出的吸引子之间的统一，以数量表示$e$-folds $N$ 被研究。在 k-essence 模型中 $L(\phi)\,X$ 形式的耦合的上下文中，我们根据标量谱指数和一般形式下的慢滚参数。为了在我们的模型中应用统一，我们考虑一些例子，以重建有效势 $V(\phi)$ 和耦合参数 $L(\phi)$ 作为暴胀子场 $\phi$ 的函数。在这里，我们发现重建分别产生了指数潜力以及自然和双曲线通货膨胀。