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Purely kinetic k-essence models have been shown in the literature to be afield theory equivalent of barotropic fluid models of dark energy or darkmatter-dark energy unification. In the modeling framework where the speed ofsound squared of a barotropic fluid is modeled as a function of its Equation ofState parameter, a systematic procedure of obtaining the Lagrangian density ofan equivalent purely kinetic k-essence model is presented. As this modelingapproach starts from the speed of sound, purely kinetic k-essence models can beconstructed for which the speed of sound is in agreement with the observationalconstraints. Depending on the chosen functional form for the barotropic fluidspeed of sound squared, analytically tractable examples of solutions for thepurely kinetic k-essence Lagrangian density in parametric and closed form areobtained.

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