Cosmological fluid dynamics in the Schr\"odinger formalism

TL;DR

This paper explores the use of the Schr"odinger formalism to model cosmological dark matter dynamics, providing analytical and numerical solutions that demonstrate its potential as an alternative to traditional methods.

Contribution

It introduces a wave-mechanical approach to cosmological fluid dynamics, including solutions for homogeneous backgrounds and overdensities, and extends to multi-fluid systems with numerical analysis.

Findings

Analytic solutions for homogeneous cosmological backgrounds.

Piecewise analytic solution for spherical overdensity evolution.

Numerical solutions for multi-fluid systems demonstrating viability.

Abstract

We investigate the dynamics of a cosmological dark matter fluid in the Schr\"odinger 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 Schr\"odinger formulation as a genuine alternative to standard methods in certain contexts, and a novel way to model multiple fluids.