Reconstructing k-essence: Unifying the attractor $n_S(N)$ and the
  swampland criteria
  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.
