Linear Newtonian perturbation theory from the Schr\"odinger-Poisson equations

TL;DR

This paper derives solutions to the Schr"odinger-Poisson equations to model cold dark matter perturbations in an expanding universe, clarifying the connections between different theoretical descriptions.

Contribution

It introduces a linear perturbation framework from the Schr"odinger-Poisson equations for cold dark matter in cosmology, highlighting regimes of equivalence among various models.

Findings

Solutions describe cold dark matter evolution in an expanding universe

Identifies regimes where different descriptions of dark matter coincide or differ

Provides a bridge between wavefunction, fluid, and scalar field models

Abstract

We obtain solutions to the coupled Schr\"odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships between descriptions of cold dark matter in terms of a pressureless fluid, in terms of a wavefunction, of a classical scalar field, and a quantum scalar field. We identify the regimes where the various descriptions coincide and where they differ.