Abstract

We study a five-dimensional non-relativistic gravity theory whose action is composed of a gravitational sector and a sector of matter where the gravitational sector is given by the so called Newton–Chern–Simons gravity and where the matter sector is described by a perfect fluid. At time to do cosmology, the obtained field equations shows a close analogy with the projectable version of the Hořava–Lifshitz theory in (3+1)-dimensions. Solutions and their asymptotic limits are found. In particular a phantom solution with a future singularity reminiscent of a Litlle Big Rip future singularity is obtained.