2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189400We generalize some of those results reported by González-Díaz by further tuning the parameter ($β$) which is closely related to the canonical kinetic term in $k$-essence formalism. The scale factor $a(t)$ could be negative and decreasing within a specific range of $β$ ($\equiv -1/ω$, $ω$ : the equation-of-state parameter) during the initial evolutional period.1 Figure, 6 pagesHigh Energy Physics - Theorytext