Expanding Universe Simulator

Expanding Universe

Matter density Ω_m 0.31

Dark energy density Ω_Λ 0.69

Hubble constant H₀ 70 km/s/Mpc

Scale factor a(t)

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H(t)

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Regime

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How it works

The Friedmann equation ties the expansion rate of a homogeneous universe to what fills it. Every galaxy cluster here sits at a fixed comoving position; the whole field is uniformly rescaled by the scale factor a(t) each frame — that stretching of space itself, not motion through it, is what drives galaxies apart (Hubble's law, v = H·d).

H(a)² = H₀²[Ωm/a³ + ΩΛ + Ωk/a²],  Ωk = 1 − Ωm − ΩΛ
da/dt = a·H(a)

Ωm — matter (ordinary + dark) dilutes as space expands, so its pull on H falls off as 1/a³; more of it slows expansion down.
ΩΛ — dark energy density stays constant as the universe grows, so once it dominates, expansion accelerates forever instead of coasting or stalling.
H₀ — today's expansion rate; it sets how fast the whole simulation runs, not its long-term fate.
When Ωm + ΩΛ > 1 the implied curvature Ωk is negative (a closed universe) and can recollapse in a Big Crunch once the term under the square root reaches zero — watch the regime label flip to "Recollapsing" and the field contract back toward the origin.

Real-world relevance: the best current fit to supernova, CMB and large-scale-structure data — the Lambda-CDM model — sits close to the default Ωm≈0.31, ΩΛ≈0.69 here, which is why that combination expands forever at a gently accelerating rate rather than recollapsing or tearing itself apart.

Observer (Milky Way) Nearby galaxies Distant galaxies

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