An Old Universe in K-Essence Cosmology

Models in which the Lagrangian contains only a kinetic factor and does not depend explicitly on the field itself in k-essence cosmology are considered. In the case of a constant potential, we obtain an exact analytic solution of k-essence, ??=−(3?−2)/3?, under a simple hypothesis, ?=?0(?/?0)?, but without any assumption about the form of ?(?). In purely kinetic k-essence model, the acceleration can only be induced after the matter-dominated epoch; the Universe is about 33.5