Purely kinetic k-essence description of $c_s^2(w)$ barotropic fluid models

TL;DR

This paper develops a systematic method to construct purely kinetic k-essence models that match observational constraints on the speed of sound in barotropic fluid dark energy models, providing analytical solutions for specific cases.

Contribution

It introduces a procedure to derive k-essence Lagrangians from the speed of sound function, enabling models consistent with observations.

Findings

Analytical solutions for k-essence Lagrangians are obtained.

The method ensures models are compatible with observational constraints.

Explicit examples demonstrate the approach's effectiveness.

Abstract

Purely kinetic k-essence models have been shown in the literature to be a field theory equivalent of barotropic fluid models of dark energy or dark matter-dark energy unification. In the modeling framework where the speed of sound squared of a barotropic fluid is modeled as a function of its Equation of State parameter, a systematic procedure of obtaining the Lagrangian density of an equivalent purely kinetic k-essence model is presented. As this modeling approach starts from the speed of sound, purely kinetic k-essence models can be constructed for which the speed of sound is in agreement with the observational constraints. Depending on the chosen functional form for the barotropic fluid speed of sound squared, analytically tractable examples of solutions for the purely kinetic k-essence Lagrangian density in parametric and closed form are obtained.