Dark matter as integration constant in Hořava-Lifshitz gravity

In the nonrelativistic theory of gravitation recently proposed by Ho\ifmmode \check{r}\else \v{r}\fi{}ava, 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 and momentum constraint equations. Consequently, classical solutions to the infrared limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity can mimic general relativity plus cold dark matter.

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