Weak singularities in large-scale structure: identification and workaround

The large-scale structure of the universe is mostly the consequence of the gravitational clustering of cold dark matter (CDM). Eventually the CDM trajectories begin to intersect ("shell-crossing"), which marks the starting point of elaborate computations in the phase-space. I show that, due to the collision-less nature of CDM, phase-space trajectories exhibit weakly singular behaviour such as local non-differentiability of the particle acceleration. Conventional N-body simulations should be able to handle these intrinsic features of perfectly cold CDM. Alternatively, singular features may be regulated by adding a finite temperature, or by employing semiclassical descriptions for the large-scale structure which I will briefly discuss.