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Phantom Divide Crossing with General Non-minimal Kinetic Coupling

We propose a model of dark energy consists of a single scalar field with a general non-minimal kinetic couplings to itself and to the curvature. We study the cosmological dynamics of the equation of state in this setup. The coupling terms have the form $ξ_{1} R f(ϕ)\partial_μϕ\partial^μϕ$ and $ξ_{2} R_{μν}f(ϕ)\partial^μϕ\partial^νϕ$ where $ξ_{1}$ and $ξ_{2}$ are coupling parameters and their dimensions depend on the type of function $f(ϕ)$. We obtain the conditions required for phantom divide crossing and show numerically that a cosmological model with general non-minimal derivative coupling to the scalar and Ricci curvatures can realize such a crossing.