Restrictions on purely kinetic k-essence

We restrict purely kinetic k-essence. Assuming the equation of state is a power law of the kinetic energy: $w=w_0X^α$, to obtain accelerated phases, we must have $α>0$ as one of necessary conditions, constrained from the conditions for stability and causality, and the k-essence must behave like phantom. We also study the evolutions of the equation of state and the speed of sound with numerical simulation.

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