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UltraDark.jl

UltraDark.jl is a tool for simulation of cosmological scalar fields, inspired by PyUltraLight and designed to be simple to use and extend.

It solves the non-interacting Gross-Pitaevskii equation

\[ i \frac{\partial \psi}{\partial t} = - \frac{1}{2m a^2} \nabla^2 \psi + m \psi \Phi\]

for a scalar field $\psi$ with mass $m$, coupled to Poisson's equation for its gravitational potential $\Phi$

\[ \nabla^2 \Phi = \frac{4 \pi G}{a} \rho = 4 \pi |\psi|^2 ,\]

where a(t) is the scale factor of the universe and $G$ is Newton's constant.

Such a scalar field describes scalar dark matter (SDM) in models including ultralight dark matter (ULDM), fuzzy dark matter (FDM), axion-like particles (ALPs) and the like. It also describes an inflaton field in the reheating epoch of the early universe.

Please open an issue if you run into problems or have feature requests.

If UltraDark contributes to your research, please cite it.

Academic articles that have used UltraDark.jl