Dark matter as integration constant in Horava-Lifshitz gravity

Abstract

In the non-relativistic theory of gravitation recently proposed by Horava, 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 Horava-Lifshitz gravity can mimic general relativity plus cold dark matter.

Comments: 16 pages; (non-)conservation equation for "dark matter" added (v2); note added to comment on some recent preprints (v3); version accepted for publication in PRD (v4)