Exact results for propagators in the geometrical adhesion model

The geometrical adhesion model that we described in previous papers provides a fully solved model for the nonlinear evolution of fields that mimics the cosmological evolution of pressureless fluids. In this context, we explore the expected late-time properties of the cosmic propagators once halos have formed, in a regime beyond the domain of application of perturbation theories. Whereas propagators in Eulerian coordinates are closely related to the velocity field, we show here that propagators defined in Lagrangian coordinates are intimately related to the halo mass function. Exact results can be obtained in the one-dimensional case. In higher dimensions, the computations are more intricate because of the dependence of the propagators on the detailed shape of the underlying Lagrangian-space tessellations, that is, on the geometry of the regions that eventually collapse to form halos. We illustrate these results for both the one-dimensional and the two-dimensional dynamics. In particular, we give here the expected asymptotic behaviors obtained for power-law initial power spectra. These analytical results are compared with the results obtained with dedicated numerical simulations.