N-body simulation and GADGET-4

The N-body idea

Cold dark matter is collisionless, so it is modelled as a set of $N$ tracer particles that interact only through gravity. Each particle feels the summed pull of all others; integrating their trajectories forward evolves the density field. The particles are not real dark-matter particles but Monte-Carlo samples of the phase-space distribution (the Vlasov flow, Topic 4.5).

Making gravity affordable

Direct summation is $O(N^2)$ — hopeless for $N\sim10^9$. Real codes use hierarchical tree methods (group distant particles and use their multipole) and particle-mesh (solve Poisson on a grid via FFT for long-range forces), often combined (TreePM). This brings the cost to $O(N\log N)$, making billion-particle boxes routine.

GADGET-4

GADGET-4 (Springel et al.) is a state-of-the-art TreePM N-body (and hydrodynamics) code. In our campaign it plays the role of the cold-dark-matter control: the same cosmological volume evolved with standard CDM physics, giving the baseline any FDM signal must be measured against.

Why it is the right control

Because the Schrödinger–Poisson system reduces to Vlasov–Poisson as $\hbar/m\to0$ (Topic 4.5), an N-body CDM code and a wave FDM code describe the same physics on large scales. That correspondence is what makes GADGET-4 a valid, apples-to-apples baseline for our wave simulations — identical initial conditions, identical cosmology, only the small-scale physics differs.