Universe Emulator — simulation

Universe Emulator: four scales in one sandbox — Friedmann equations from Planck time, an N-body dark-matter web, a galaxy that badly needs its halo, and a real solar system on JPL elements. Not one canned animation: every number on screen follows from the parameters you set.

The cosmos runs on Friedmann: H²(a) = H₀²[Ωᵣa⁻⁴ + Ωₘa⁻³ + Ωₖa⁻² + ΩΛ], and the curvature Ωₖ = 1 − Ωᵣ − Ωₘ − ΩΛ is derived, never typed in. The age of the universe is the integral of 1/H from a to infinity: a 900-node log grid, Simpson per interval, log-log interpolation, because bisecting an integral cannot keep up with a slider dragged across forty orders of magnitude. Out of the same machinery come the particle horizon, the deceleration parameter q, the CMB temperature T = 2.7255/a, the growth factor D(a) and the density budget. Twelve epochs, from 10⁻⁴³ seconds to the far future, and the last two are rewritten for whatever fate the parameters actually give: a bounce instead of a Big Bang, the Big Crunch, heat death, the Big Chill, eternal coasting. A universe with Ωₘ = 2.2 at ΩΛ = 0 really does collapse, and the caption on screen says exactly that.

The web is an honest N-body run, not a picture of filaments: 21³ = 9261 particles in a comoving box, gravity through a Barnes–Hut tree at θ = 0.7, softening about a third of the mean interparticle spacing — tighter and two-body scattering heats the box, looser and there are no filaments. The initial field is a sum of 28 plane waves with falling amplitude: that is what produces sheets and threads rather than uncorrelated speckle. Particles sit a quarter of a spacing off the lattice: a perfect crystal is not merely ugly, it transmits impulses along its lines of centres, and those artefacts look like structure that gravity made. Velocities come from the growing mode p = a²ḟ·x, expansion is divided out exactly, and σ(δ) is measured on a 4-16 cell grid with the shot noise 1/mean subtracted — otherwise the number would report how many particles there are, not how they are spread.

The galaxy is assembled from profiles, not drawn: an exponential disc of 6×10¹⁰ solar masses with a 3 kpc scale length, a 10¹⁰ Plummer bulge, an NFW halo with 10¹² inside r₂₀₀ and concentration 12. Three and a half thousand test stars integrate in a smooth field (G = 0.04499 kpc³ per 10¹⁰ solar masses per Myr²), 26 Myr of galactic time to a screen second. The rotation curve is read at the Sun's radius, 8 kpc: 230 km/s with the halo, 171 without it, and that is precisely the difference dark matter was invented for. The halo's share inside the Sun's orbit is about 45 %, computed from the profiles rather than plugged in.

The system is eight planets on approximate JPL elements: position comes from Kepler's equation, solved for the anomaly by Newton, and years count from J2000, so the date on screen is a real date. The radial scale is compressed to the 0.4 power so Mercury stays visible next to Neptune; order and the shape of the ellipses survive it, and a toggle gives the honest scale. Launching a rogue star hands the planets to direct summation over ten bodies (step 2.5 thousandths of a year, roughly a day per step; two years of the fly-by per screen second): an intruder of 0.6 solar masses starts at 42 AU, outside Neptune's orbit, aiming 6 AU off the Sun at 2.2 AU per year. A body counts as ejected not by distance — aphelion is far in any case — but by positive orbital energy relative to the Sun.

All of it is drawn on a plain 2D canvas: no WebGL, no shaders, no external library. The colour of the early universe is a blackbody approximation by Tanner Helland, and it genuinely is whitish at 10⁹ K and dim red at the 3000 K surface of last scattering; from there the same colour slides into the red with the redshift. The charts (a(t), the density budget, σ(δ)) are drawn by a small internal module with logarithmic axes. Star scatter, filaments and the falling star all come from one seed text, so a link in the address bar reproduces the universe to the digit: the tab, the seed and all four Friedmann parameters live in it.

Rules:

You cannot lose here, but you cannot make the model lie either: the number on screen comes from equations, not from a nice table. Sliders: H₀ 20-140 km/s/Mpc, Ωₘ 0-3, ΩΛ from minus 1 to 4, Ωᵣ up to 40×10⁻⁵, curvature is derived. The system has eight planets, any date, and one rogue star at a time. Past a = 10⁴ the history stops: the universe is dead there, and the clock honestly stands still.

How to play:

Space pauses, arrows switch the four tabs; the tab and the seed go into the address bar, so a universe travels as a link. The time slider scrubs the history, seven presets set complete models. The web turns under mouse or finger, tilt is a slider, Run to today integrates down to z = 0. The galaxy: dark matter toggle, disc and halo masses, viewing angle. The system: a planet picker, days per second, a rogue star.

Tips:

Start on the Planck 2018 preset, then set Ωₘ = 2.2 at ΩΛ = 0: the universe collapses and the late epoch captions rewrite themselves. Switch the halo off and watch the rotation curve drop from 230 to 171 km/s. Run the web to today and compare σ(δ) before and after — gravitational instability in one number. Launch a rogue star on other seeds: two to four planets escape, never the same ones.