Wave mechanics and the adhesion approximation
Abstract
The dynamical equations describing the evolution of a selfgravitating fluid of cold dark matter (CDM) can be written in the form of a Schrödinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasilinear regime, the Schrödinger equation can be reduced to the exactly solvable freeparticle Schrödinger equation. The freeparticle Schrödinger equation forms the basis of a new approximation scheme—the freeparticle approximation—that is capable of evolving cosmological density perturbations into the quasilinear regime. The freeparticle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a nonlinear term known as the quantum pressure. Simple onedimensional tests of the freeparticle method have yielded encouraging results. In this paper we comprehensively test the freeparticle approximation in a more cosmologically relevant scenario by appealing to an Nbody simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the freeparticle approximation comprehensively outperforms both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 December 2006
 DOI:
 10.1088/14757516/2006/12/016
 arXiv:
 arXiv:astroph/0605013
 Bibcode:
 2006JCAP...12..016S
 Keywords:

 Astrophysics
 EPrint:
 27 pages, 8 figures. Shortened to 19 pages, 7 figures. Restructured with some changed content. Title changed accordingly