  At the present work, it is studied the extension of F (R) gravities to the
new recently proposed theory of gravity, the so-called Horava-Lifshitz gravity,
which provides a way to make the theory power counting renormalizable by
breaking Lorentz invariance. It is showed that dark energy can be well
explained in the frame of this extension, just in terms of gravity. It is also
explored the possibility to unify inflation and late-time acceleration under
the same mechanism, providing a natural explanation the accelerated expansion.
