Erlangen 2026 – scientific programme

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GR: Fachverband Gravitation, Relativistische Astrophysik und Kosmologie

GR 18: Cosmology III

GR 18.1: Talk

Friday, March 20, 2026, 11:00–11:15, KH 01.016

Effective Pressure and Viscosity Analogies in Schrödinger*Poisson Models of Structure Formation — •Aoibhinn Gallagher — Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany

Recent advances in wave-mechanical approaches to cosmic structure formation have highlighted the usefulness of the Schrödinger*Poisson (or Schrödinger*Newton) system as an alternative description of collisionless matter. Beyond its role in models of ultra-light dark matter, this framework offers a compact way to capture gravitational dynamics across linear and non-linear regimes, motivating renewed interest in how its behaviour relates to familiar concepts from classical physics.

In this talk, I explore how certain features of Schrödinger*Newton evolution can be reinterpreted through the lens of classical fluid dynamics, in particular through effective *pressure* and *viscosity* analogies. I show that the parameter \nu, often introduced in practical implementations of the formalism, can play a role akin to a kinematic viscosity, and I assess when a pseudo-Reynolds number description becomes meaningful. This reinterpretation provides intuitive insight into non-linear structure formation, especially beyond shell-crossing where standard fluid approaches fail. At the same time, I outline the fundamental limitations of the analogy: a full classical fluid correspondence would require additional physical ingredients (such as dissipation and entropy production) that do not arise in strictly unitary Schrödinger*Newton dynamics. The resulting picture is therefore not a complete fluid model, but a useful heuristic framework that clarifies the behaviour of wave-mechanical cosmological systems.

Keywords: Wave-mechanics; Fluid-dynamics; Structure-formation; Cosmology; Dark matter