Cosmological solutions in F(R) Horava-Lifshitz gravity

Emilio Elizalde, Shin'ichi Nojiri, Sergei D. Odintsov, Diego Saez-Gomez

Recently a new proposal of gravitational theory has been suggested by Horava, which looks to be power counting renormalizable, due to the theory introduces an anisotropy in the temporal coordinate that makes the theory to not be invariant under general diffeomorphisms. Here we extend this theory to more general actions that could provide interesting results in the cosmic evolution as well as we explore the possible consequences of the new parameters of the theory that naturally appear when the diffeomorphism invariance is lost. We show that, as in the classical F(R) theory, cosmic acceleration can be well explained with no need of any dark energy component, and even the inflationary epoch may be produced by the same mechanism. The aims and problems of the theory will be discussed.