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Caustics are formally singular structures, with infinite density, that formin collisionless media. The non-negligible velocity dispersion of dark matterparticles renders their density finite. We evaluate the maximum density of thecaustics within the framework of secondary infall model of formation of darkmatter haloes. The result is then used to demonstrate that caustics can beprobed by properly stacking the weak-lensing signal of about 600 haloes. CFHTLSaccompanied by X-ray observations and the space-based experiments like SNAP orDUNE can provide us with the required statistics and hence a way ofdistinguishing between the viable dark matter particle candidates. Theextension of our results to more realistic models including the effects ofmergers of haloes is briefly outlined.Comment: Minor changes, two references added, 6 pages, 3 figures, to appear in  Proc. 21st IAP Colloquium "Mass Profiles and Shapes of Cosmological  Structures", Paris 4-9 July 2005, [EAS Publications Series, eds: G. Mamon, F.  Combes, C. Deffayet, B. Fort

Caustics in dark matter haloes