Exact Results for Propagators in the Geometrical Adhesion Model

TL;DR

This paper derives exact and asymptotic results for propagators in the Geometrical Adhesion Model, linking them to halo formation and the halo mass function, validated through numerical simulations in 1D and 2D.

Contribution

It provides the first exact solutions for propagators in the GAM, especially in 1D, and explores their relation to halo properties in higher dimensions.

Findings

Exact propagator results in 1D GAM

Asymptotic behaviors for power-law spectra

Numerical validation of analytical results

Abstract

The Geometrical Adhesion Model (GAM) we described in previous papers provides a fully solved model for the nonlinear evolution of fields that mimic 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 1D case. In higher dimensions, the computations are more intricate because of to 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 1D and the 2D 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.