Dark matter as integration constant in Hořava-Lifshitz gravity

In the non-relativistic theory of gravitation recently proposed by Hořava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like pressureless dust emerges as an “integration constant” of dynamical equations. Consequently, classical solutions to the infrared limit of Hořava-Lifshitz gravity can mimic general relativity plus cold dark matter.