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We develop a theoretical framework for describing the hierarchical structureof the phase space of cold dark matter haloes, due to gravitationally boundsubstructures. Because it includes the full hierarchy of the cold dark matterinitial conditions and is hence complementary to the halo model, the stableclustering hypothesis is applied for the first time here to the small-scalephase space structure. As an application, we show that the particle dark matterannihilation signal could be up to two orders of magnitude larger than that ofthe smooth halo within the Galactic virial radius. The local boost is inverselyproportional to the smooth halo density, and thus is O(1) within the solarradius, which could translate into interesting signatures for dark matterdirect detection experiments: The temporal correlation of dark matter detectioncan change by a factor of 2 in the span of 10 years, while there will besignificant correlations in the velocity space of dark matter particles. Thiscan introduce O(1) uncertainty in the direction of local dark matter wind,which was believed to be a benchmark of directional dark matter searches or theannual modulation signal.

Hierarchy in the Phase Space and Dark Matter Astronomy