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

TL;DR

This paper reconstructs a k-essence inflationary model unifying swampland criteria with observational data, deriving potential and coupling functions that include exponential, natural, and hyperbolic inflation scenarios.

Contribution

It introduces a formalism to unify swampland constraints with the scalar spectral index and slow roll parameters in k-essence inflation models, providing explicit reconstructions of potentials and couplings.

Findings

Reconstructed exponential, natural, and hyperbolic inflation potentials.

Unified theoretical framework linking swampland criteria with observational parameters.

Demonstrated the viability of unifying fundamental theory with observational data in inflation models.

Abstract

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.