Caustic avoidance in Hořava-Lifshitz gravity

There are at least four versions of Hořava-Lishitz gravity in the literature. We consider the version without the detailed balance condition with the projectability condition and address one aspect of the theory: avoidance of caustics for constant time hypersurfaces. We show that caustics cannot form with codimension one in the absence of matter source if λ deviates from 1 near would-be caustics via RG flow. We argue that inclusion of matter source will not change the conclusion. We also argue that caustics with codimension higher than one will not form because of repulsive gravity generated by nonlinear higher curvature terms. Finally, we discuss implications to the recently proposed scenario of “dark matter as integration constant”.