This is a flat top-down companion to the 3D balloon-analogy simulator: same expanding-space idea, but here the scale factor comes from an exact matter-dominated flat-FRW (Einstein–de Sitter) solution instead of the 3D scene's illustrative exponential, so a real "time since Big Bang" slider makes sense:
a(t) = (t / t₀)^(2/3) H(t) = ȧ/a = 2/(3t)
t₀ = 2/(3H₀) ← age of the universe implied by H₀
Every dot sits at a fixed comoving position — it never moves in comoving coordinates. What you see spread apart is space itself stretching: physical position = comoving position × a(t). Click any two dots to pick an observer (yellow) and a target (cyan); the panel reports their proper distance d(t) and recession velocity v = H(t)·d(t) — Hubble's law, which holds for an observer sitting on any dot, not just one at the centre.
- H₀ — today's expansion rate; a higher H₀ means a younger, faster-expanding universe (t₀ shrinks as 1/H₀).
- t — time since the Big Bang; near t=0 all dots collapse toward the origin (the singularity), and dragging past t₀ shows the universe continuing to expand into the future.
This matter-only model gives a smaller age (~9.3 Gyr at H₀=70) than the real ΛCDM universe (~13.8 Gyr) because it omits dark energy's late-time acceleration — it is kept simple on purpose to make the H₀↔age relationship exact and easy to verify by hand, exactly like the 3D scene's own simplified exponential.