Cosmic Expansion & Structure Simulator

Expanding Universe

Hubble constant H₀ 67 km/s/Mpc

Matter density Ωm 0.31

Perturbation strength 1.0×

Time speed 1.0×

Scale factor a

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Cosmic age

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H(a)

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Expansion

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How it works

Each galaxy sits on a fixed comoving grid point q and is displaced by a superposition of plane waves scaled by a growth factor D(a): x(a) = a·[q + D(a)·Ψ(q)]. This is the Zel'dovich approximation — the same first-order technique cosmologists use to seed N-body simulations of the cosmic web. The multiplying a stretches the whole grid apart (uniform Hubble expansion), while D(a) amplifies the wiggles in Ψ so overdense regions collapse into filaments and clusters while underdense regions empty into voids. Colour encodes the local density contrast δ = −D(a)·∇·Ψ.

(ȧ/a)² = H₀²[Ωm/a³ + ΩΛ],  ΩΛ = 1 − Ωm
x(q,a) = a·[q + D(a)·Ψ(q)],  D(a) ≈ a

Hubble constant H₀ — sets today's expansion rate; higher H₀ ages the universe faster for the same scale factor.
Matter density Ωm — the matter/dark-energy split (ΩΛ = 1 − Ωm). High Ωm decelerates expansion and favours collapse; low Ωm hands the tug-of-war to dark energy, which stretches space and freezes structure growth.
Perturbation strength — amplitude of the initial density field; stronger seeds produce sharper filaments and deeper voids at the same age.
Time speed — playback multiplier; the underlying Friedmann integration is exact regardless of this setting.

Real-world relevance: this is the same competition — matter's self-gravity trying to build structure, dark energy's negative pressure trying to tear it apart — that determines whether today's cosmic web keeps growing or, as observed, gradually freezes as dark energy takes over.

Overdense (filament/cluster) Underdense (void)

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