Unifying inflation with dark energy in modified F(R) Horava-Lifshitz gravity

We study FRW cosmology for a non-linear modified F® Horava-Lifshitz gravity which has a viable convenient counterpart. A unified description of early-time inflation and late-time acceleration is possible in this theory, but the cosmological dynamic details are generically different from the ones of the convenient viable F® model. Remarkably, for some specific choice of parameters they do coincide. The emergence of finite-time future singularities is investigated in detail. It is shown that these singularities can be cured by adding an extra, higher-derivative term, which turns out to be qualitatively different when compared with the corresponding one of the convenient F® theory.