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There is a vast menagerie of plausible candidates for the constituents ofdark matter, both within and beyond extensions of the Standard Model ofparticle physics. Each of these candidates may have scattering (and other)cross section properties that are consistent with the dark matter abundance,BBN, and the most scales in the matter power spectrum; but which may havevastly different behavior at sub-galactic "cutoff" scales, below which darkmatter density fluctuations are smoothed out. The only way to quantitativelymeasure the power spectrum behavior at sub-galactic scales at distances beyondthe local universe, and indeed over cosmic time, is through probes available inmultiply imaged strong gravitational lenses. Gravitational potentialperturbations by dark matter substructure encode information in the observedrelative magnifications, positions, and time delays in a strong lens. Each ofthese is sensitive to a different moment of the substructure mass function andto different effective mass ranges of the substructure. The time delayperturbations, in particular, are proving to be largely immune to thedegeneracies and systematic uncertainties that have impacted exploitation ofstrong lenses for such studies. There is great potential for a coordinatedtheoretical and observational effort to enable a sophisticated exploitation ofstrong gravitational lenses as direct probes of dark matter properties. Thisopportunity motivates this white paper, and drives the need for: a) strongsupport of the theoretical work necessary to understand all astrophysicalconsequences for different dark matter candidates; and b) tailoredobservational campaigns, and even a fully dedicated mission, to obtain therequisite data.

Strong gravitational lensing probes of the particle nature of dark matter