Cosmological fluid dynamics in the Schrödinger formalism

Johnston, Rebecca; Lasenby, A. N.; Hobson, M. P.

Cosmological fluid dynamics in the Schrödinger formalism

Authors

Johnston, Rebecca

Lasenby, A. N.

Hobson, M. P.

Description

We investigate the dynamics of a cosmological dark matter fluid in the Schrödinger formulation, seeking to evaluate the approach as a potential tool for theorists. We find simple wave-mechanical solutions of the equations for the cosmological homogeneous background evolution of the dark matter field, and use them to obtain a piecewise analytic solution for the evolution of a compensated spherical overdensity. We analyse this solution from a `quantum mechanical' viewpoint, and establish the correct boundary conditions satisfied by the wavefunction. Using techniques from multi-particle quantum mechanics, we establish the equations governing the evolution of multiple fluids and then solve them numerically in such a system. Our results establish the viability of the Schrödinger formulation as a genuine alternative to standard methods in certain contexts, and a novel way to model multiple fluids.
12 pages, 8 figures, submitted to MNRAS