Wave mechanics and the adhesion approximation

Abstract

The dynamical equations describing the evolution of a self-gravitating fluid of cold darkmatter (CDM) can be written in the form of a Schrödinger equation coupled to a Poissonequation describing Newtonian gravity. It has recently been shown that, in the quasi-linearregime, the Schrödinger equation can be reduced to the exactly solvable free-particleSchrödinger equation. The free-particle Schrödinger equation forms the basis of a newapproximation scheme—the free-particle approximation—that is capable of evolvingcosmological density perturbations into the quasi-linear regime. The free-particleapproximation is essentially an alternative to the adhesion model in which the artificialviscosity term in Burgers’ equation is replaced by a non-linear term known as thequantum pressure. Simple one-dimensional tests of the free-particle method haveyielded encouraging results. In this paper we comprehensively test the free-particleapproximation in a more cosmologically relevant scenario by appealing to anN-body simulation. We compare our results with those obtained from two establishedmethods: the linearized fluid approach and the Zeldovich approximation. Wefind that the free-particle approximation comprehensively out-performs both ofthese approximation schemes in all tests carried out and thus provides anotheruseful analytical tool for studying structure formation on cosmological scales.