Cosmology in (1+1)-dimensional Horava-Lifshitz theory of gravity

The (1 + 1)-dimensional Friedmann-Robertson-Walker universe filled with a perfect fluid with equation of state p = omega rho is analyzed through the view of Horava-Lifshitz (HL) theory of gravity. In this theory, the anisotropic scaling of space and time breaks Lorentz invariance of general relativity in such a way that the gravitational action is no longer a topological invariant and the theory becomes dynamical. With the introduction of a perfect fluid through Schutz formalism, it is shown that the resulting dynamical theory is very similar to the two-dimensional Jackiw-Teitelboim model, where a dilatonic degree of freedom is introduced to force a dynamical theory. However, in HL theory, the introduction of a dilaton field is not necessary.