Big Bang Expansion Simulator

Big Bang Expansion

Hubble constant H₀ 70 km/s/Mpc

Matter density Ω_m 0.31

Playback speed 0.15 Gyr/s

Scale factor a(t)

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Age of universe

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Radiation temperature T(t)

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How it works

The scale factor a(t) measures how much a fixed comoving distance has stretched since the value it is pinned to today, a(now) = 1. Its evolution follows straight from the Friedmann equation for a flat universe made of radiation, matter and a cosmological constant (dark energy):

H(a)² = H₀² · ( Ω_r / a⁴ + Ω_m / a³ + Ω_Λ )
da/dt = a · H(a)
T(a) = T₀ / a

Each density term fades at a different rate as a grows, so it dominates the dynamics in turn: radiation (a⁻⁴) ruled the hot early universe, matter (a⁻³) took over and decelerated the expansion for billions of years, and the constant Ω_Λ term — negligible early on — now dominates and drives the accelerating expansion measured today. The sim integrates this ODE live with RK4 every frame, starting just after recombination (a ≈ 0.00091, T ≈ 3000 K, the redshift at which the plasma became transparent and released the light we see as the CMB).

Hubble constant H₀ — today's expansion rate; a larger value compresses the whole timeline into a younger, faster-expanding universe.
Matter density Ω_m — the flat-universe constraint fixes Ω_Λ = 1 − Ω_m − Ω_r, so this slider trades matter's deceleration against dark energy's acceleration and shifts when the transition between them happens.
Playback speed — how many billion years of cosmic time elapse per real second.
Inflation burst — an illustrative few seconds of pure exponential growth, a(τ) = a₀e^(H_inf·τ), played before the Friedmann integration begins, standing in for the inflationary epoch (which really lasted a fraction of the first second and is not visualizable to true scale).

Real-world relevance: this is the same equation used to build the standard ΛCDM cosmological model that fits the observed cosmic microwave background, galaxy redshifts and supernova brightness — it is not a toy formula, just a live numerical solve of it.

Protogalaxy cluster Recombination glow Comoving grid

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