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Cosmological simulations and surveys · 1774–2026

Simulated Universes

No one will ever watch a galaxy form. It takes billions of years, and we arrived late. So we build universes instead, out of particles and equations, and run them forward on the largest machines we have, to see whether what grows there looks like the sky.

This is a gallery of those universes: 166 entries: simulations, their ancestors and the codes that run them, beside the 103 surveys of the real sky they are held up against.

The Universe Being Simulated

Before the machines, the thing they imitate: what galaxies are, how many there are, and how they were found to gather into the largest structures known.

Island Universes For a thousand years, faint smudges of light hung in the sky. In 1925 they turned out to be other galaxies, millions of light-years away.

On a dark night, without any instrument, three smudges can be seen that are not stars. In the north, a faint oval in Andromeda. In the south, two pale clouds, as if torn from the Milky Way. People have looked at them for as long as there have been people. For a thousand years after al-Sufi wrote down the first, no one knew what they were.

  1. 964al-SufiThe Book of Fixed Stars records Andromeda as a “small cloud”: the oldest known written mention of another galaxy.
  2. 1502–1522Vespucci, PigafettaEuropean sailors describe the two clouds of the southern sky, long named and storied by Aboriginal Australian and Māori peoples.
  3. 1750–1755Wright, KantFaint nebulae might be whole systems of stars like our own: the idea later called island universes.
  4. 1771–1781MessierA catalogue of fuzzy objects so comet hunters would not be fooled. Andromeda is M31.
  5. 1845Lord RosseWith a 1.8 m telescope in Ireland, the first spiral is seen and drawn: M51, the Whirlpool.
  6. 1912Henrietta LeavittPulsating stars in the Small Magellanic Cloud reveal a law linking period to brightness: the yardstick for cosmic distance.
  7. 1920Shapley and CurtisThe Great Debate: is our galaxy the whole Universe, or one among many?
  8. 1925Edwin HubbleCepheids in Andromeda place it far beyond the Milky Way. The Universe is suddenly far larger than our galaxy.
  9. 1927–1929Lemaître, HubbleThe farther a galaxy, the faster it recedes. The Universe is expanding.

The answer, when it came, was vertiginous. Andromeda is a city of about a trillion stars, some 150,000 light-years wide, whose light left it about 2.5 million years ago. The Magellanic Clouds are smaller galaxies orbiting ours, 160,000 and 200,000 light-years away. And the Milky Way itself, a disc about 100,000 light-years across with a few hundred billion stars, is one galaxy among a number that would take another century to estimate.

A Census of Everything We Can See 13.8 billion years, hundreds of billions of galaxies, perhaps a trillion trillion stars, and most of the mass invisible.

Everything below lies inside our past light cone: the part of the Universe whose light has had time to reach us. These are the numbers every simulation is built to reproduce.

Age
13.8billion years

Planck 2018: 13.787 ± 0.020

Observable radius
46.5billion light-years

Larger than the age, because space stretched while the light travelled

Galaxies
1011–1012

Hundreds of billions (New Horizons, 2021) to about two trillion (Conselice and colleagues, 2016)

Stars
1022–1024

A rough product of stars per galaxy and galaxies

Atoms
~1080

About 1.5 × 1053 kg of ordinary matter, an order-of-magnitude estimate

Oldest light
2.725kelvin

The cosmic microwave background today, released at redshift 1,090

What the Universe is made of today (Planck 2018)

4.9% ordinary matter: every star, planet, cloud and person

Where the ordinary matter is (Fukugita and Peebles 2004)

6% in stars 4% hot gas in clusters

Dark matter outweighs ordinary matter by about five to one, and most ordinary matter is not in stars at all but in thin gas between galaxies, so faint it was counted only in 2020, using the delay of fast radio bursts crossing it. The two great uncertainties are spelled out on purpose. The number of galaxies depends on how many faint dwarfs exist beyond what any telescope sees; the latest measurements lean toward hundreds of billions. And the expansion rate measured nearby, about 73 kilometres per second per megaparsec, disagrees with the 67 inferred from the early Universe: the Hubble tension, still unresolved.

The Architecture of the Sky From Shapley's cloud of galaxies in 1930 to Laniakea, our home supercluster: how the cosmic web was found.

Galaxies are not scattered like dust. Throughout the twentieth century, each new survey found larger patterns: clusters, then superclusters, then voids and walls, then flows of galaxies converging on hidden masses.

  1. 1930Harlow ShapleyA southern survey finds “the most striking concentration of galaxies” in Centaurus, today the Shapley Supercluster.
  2. 1933Fritz ZwickyGalaxies in the Coma cluster move too fast for the visible mass to hold them. He calls the missing mass “dunkle Materie”.
  3. 1953Gérard de VaucouleursThe crowd of galaxies around Virgo is a flattened super-system: the Local Supercluster.
  4. 1958George Abell2,712 rich clusters catalogued from the Palomar plates.
  5. 1978Gregory and Thompson; Jõeveer, Einasto and TagoThe first voids: great regions empty of galaxies in front of the Coma supercluster and between southern superclusters.
  6. 1981Kirshner and colleaguesThe Boötes Void: a region about 400 million light-years across, nearly empty. Later surveys found about sixty galaxies where some two thousand would be expected.
  7. 1986–1989de Lapparent, Geller, HuchraA slice of the Universe shows galaxies on the walls of bubbles, and the Great Wall across the northern sky.
  8. 1988The “Seven Samurai”Galaxies stream toward a hidden mass behind the Milky Way's disc: the Great Attractor.
  9. 2003Gott, Jurić and colleaguesThe Sloan Great Wall, about 1.4 billion light-years long.
  10. 2005SDSS and 2dFGRS teamsBaryon acoustic oscillations: a sound wave from the young Universe, frozen into the spacing of galaxies.
  11. 2014Tully, Courtois, Hoffman, PomarèdeMapping galaxy motions defines our home: Laniakea, “immense heaven” in Hawaiian, about 520 million light-years across.
  12. 2023Tully, Howlett, PomarèdeHoʻoleilana, “sent murmurs of awakening”, a name from the Kumulipo creation chant: a shell of galaxies about a billion light-years across, some 820 million light-years away, proposed as a single frozen sound wave of the young Universe. A claim still being tested.
  13. 2024Valade and colleaguesCosmicflows-4 basins: a slight preference for Laniakea being part of the larger Shapley basin. A hint, not a verdict.
  14. 2025Böhringer and colleaguesQuipu, the largest structure yet found in the nearby Universe: about 1.3 billion light-years long.

The search for ever larger structures has a limit. Averaged over spheres about 300 million light-years in radius, the Universe becomes smooth, the same everywhere: the “end of greatness” measured by SDSS and WiggleZ. Claims of structures far beyond that scale, like a ten-billion-light-year wall traced by gamma-ray bursts, remain contested. This is exactly the regime simulations are built to explore: the cosmic web grows in them from the same rules, and the largest boxes are big enough to contain the end of greatness many times over.

A Ladder of Scales From our galaxy to the edge of the observable Universe, on one ruler.
Milky Way discabout 100,000 ly across
Distance to the Large Magellanic Cloudabout 163,000 ly
Distance to Andromedaabout 2.5 million ly
Local Superclusterabout 110 million ly across
BAO rulerabout 490 million ly
Laniakeaabout 520 million ly across
Quipuabout 1.3 billion ly long
Observable Universeabout 93 billion ly across
Logarithmic scale: every factor of ten adds the same length to a bar, from 30,000 to 160 billion light-years. ly = light-years.

A simulation box sits somewhere on this ladder. The zoom-ins that model a single Milky Way look at the first rungs; the flagship volumes span the middle; the largest runs reach across billions of light-years, a sizeable fraction of everything we can see.

A Primer on Simulated Universes

Eight short explainers, from the reason these machines exist to the numbers on each card. Open any one. Underlined words show their meaning when you point at them.

Why Build a Universe We cannot rerun the cosmos or wait billions of years, so we grow copies of it in computers and compare them with the sky.

Astronomy has a peculiar handicap. Chemists can repeat an experiment; biologists can watch a cell divide. Astronomers get one Universe, seen from one place, at one moment of its 13.8-billion-year history. Every galaxy we see is a single frame of a film that runs far too slowly to watch.

A simulation turns that frame into a film. Put the right ingredients in a box, apply the laws of physics, and let the computer run time forward. If the result looks like the real sky, in the number of galaxies, their shapes, how they cluster, the theory that built it survives. If not, something is missing.

  • Test theories. The standard model of cosmology, ΛCDM, makes predictions that only a simulation can work out in detail.
  • Read the sky. To know what a telescope sees, you need to know what a galaxy of a given age and mass should look like.
  • Rehearse surveys. Missions like Euclid or the Rubin Observatory are tested on mock catalogues before the real data arrive.
  • Watch the unseeable. Dark matter, the first stars, the slow assembly of the Milky Way: none can be watched directly.
The Recipe Start from the faint ripples of the early Universe, let gravity and expansion act, save snapshots, compare.
  1. SeedsTiny ripples, measured in the cosmic microwave background.
  2. BoxParticles laid on a grid in a comoving cube and nudged by the ripples.
  3. GravityEach step, every particle feels every other while space expands.
  4. PhysicsOptionally gas, stars, black holes, magnetic fields, light.
  5. SnapshotsThe state of everything, saved at chosen moments.
  6. CompareFind halos and galaxies, measure them, hold them up to the sky.

The initial conditions are the one part not invented: their statistics come from measurements of the early Universe. From there the computer advances in thousands of small time steps, from a redshift of a few tens to a few hundred down to today. The box wraps around on itself, so matter leaving one face re-enters from the opposite side, as if the box were one tile of an endless floor.

The Invisible Scaffolding Most matter is dark. Its gravity weaves a web of clumps and threads, and galaxies light up where the threads meet.

About five sixths of all matter is dark matter. Nobody knows what it is, but its gravity is unmistakable, and in a simulation it does most of the work. Starting almost smooth, it drains out of the emptier regions and piles up in the denser ones. The result is the cosmic web: round halos at the knots, long filaments between them, and great voids in between.

Gas follows the dark matter, falls into the halos, cools and forms stars. That is why a dark-matter-only run, the cheapest kind, can still say a lot about galaxies: it tells you where they will be. Halos merge, and the small ones that fall into big ones survive for a while as subhalos, the homes of satellite galaxies.

Particles, Grids, Meshes Every code chops space or matter into pieces. How it chops decides what it sees well and what it blurs.
N-body particles
Particle-mesh grid
Tree or adaptive mesh
Moving mesh

Schematic drawings, not data.

Gravity is the easy physics and the hard sum. With N particles there are about N²/2 pairs, which for ten billion particles is fifty billion billion. Codes cheat cleverly. A grid computes gravity in one sweep but blurs anything smaller than a cell. A tree lumps distant particles together and treats them as one. Most modern codes mix the two (TreePM) or go further with the fast multipole method.

Gas is harder, because it has pressure, shocks and turbulence. SPH treats it as particles; adaptive meshes refine a grid where needed; the moving mesh of AREPO and the meshless schemes of GIZMO sit between. Each leaves its own fingerprint, which is why the same physics run through two codes never gives quite the same galaxy.

Wide Field or Sharp Eye A computer has a fixed budget: spend it on a huge box seen coarsely, or on one galaxy seen finely.
A coarse box, and one region re-run in fine detail: a zoom-in. Schematic.

The number of particles a machine can follow is roughly fixed. Spread them over a box billions of light-years wide and each particle weighs as much as a whole galaxy: you see the cosmic web, rare giant clusters, the statistics a survey needs, but no galaxy's inner life. Pack them into a small box and you see spiral arms and star-forming clouds, but only a handful of objects, and never the rarest ones.

The zoom-in is the way out: simulate a large region coarsely, choose one halo, and re-run only its surroundings at far higher mass resolution. Aquarius, Auriga, FIRE and many others are zooms. The big volumes, Millennium, FLAMINGO, Uchuu, give the census. The two kinds need each other.

What the Grid Cannot See Stars and black holes are far smaller than a simulation's pixels, so their effects are added by rules. Those rules are where projects differ most.

The sharpest dwarf-galaxy zooms now reach a few suns and form stars one by one, but most cosmological runs have resolution elements of thousands of suns, and the big volumes millions or more: far coarser than a single star or the region around a black hole. Whatever happens below that scale, a star being born, a supernova, a black hole swallowing gas, is added through subgrid physics: rules saying, in effect, "when gas is this dense and cold, turn some of it into stars".

The most important rules concern feedback. Exploding stars and growing black holes (active galactic nuclei) pour energy back into the gas. Without it, simulated galaxies come out far too massive and too compact. With it, they start to look right. Most projects calibrate a few parameters against observations, then treat everything else as a prediction. Others, like FIRE, push resolution high enough to model individual supernovae more directly. Either way, part of every galaxy formation simulation is a model, not a law, and the best ones say so plainly.

Reading a Card What a box size, a particle count, a redshift and a mass resolution actually tell you.
Box
Side of the cube, usually in megaparsecs, often divided by little h. A thousand megaparsecs is over three billion light-years.
Particles
How many pieces the matter is cut into. Written as a cube when particles start on a grid: 2160³ is about ten billion.
Mass resolution
Mass of one particle, in solar masses. The smaller, the finer the detail.
Runs to
The last moment simulated. Redshift 0 is today; runs of cosmic dawn stop near redshift 5 or 6, when the Universe was about a billion years old.
Compute
Total processor time. The largest runs need tens or hundreds of millions of CPU-hours on national supercomputers.
Softening
Not on every card, but behind every number: below this distance a run's gravity is deliberately blurred.
Open Questions Simulations match the large-scale Universe remarkably well. At the smallest scales and in a few measurements, tensions remain.

On large scales the agreement is striking: simulated cosmic webs match the clustering of millions of real galaxies. Closer in, questions remain. Dark-matter-only runs once predicted many more satellite galaxies, and denser galaxy centres, than are observed; better feedback and better surveys have softened these problems without fully closing them. Some measurements of how clumpy matter is today come out slightly lower than the early-Universe prediction, a tension simulations with neutrinos and stronger feedback are now probing.

Cost is the other limit. One flagship run can occupy a national supercomputer for months. That is why the field now builds suites of hundreds of smaller runs and trains emulators on them, and why machine learning is beginning to stand in for parts of the computation itself.

COLIBRE · one slab, eight lights

Anatomy of a Simulated Universe

A slice of a simulated universe 400 megaparsecs wide, 1.3 billion light-years, and 10.5 megaparsecs thick, flattened into one picture. It shows the Universe about 1.3 billion years ago, close to today on cosmic timescales. Change the light you see it by, compare two lights, and open the structures the web is made of.

The cosmic web in a COLIBRE simulation slab, shown as gas density: bright threads and knots around dark voids.

Light

Where the ordinary matter is. Most of it is thin gas between the galaxies, drawn into the same threads as the dark matter. Bright means dense.

Compare

Read the web

What you are looking at

Each picture adds up or averages everything in a slab 10.5 megaparsecs deep, as if looking down through a thick sheet of space. Dark matter has drawn the gas into a web of filaments and knots around wide voids. The landmarks mark eight kinds of structure; open any of them, or take the tour.

How much of what

Share of this slab's area and dark matter in each class, beside the most quoted three-dimensional census.

Area hereVolume, 3DMass hereMass, 3D
Voids 70%77%19%15%
Walls 12%18%14%24%
Filaments 17%6%40%50%
Nodes <1%<1%27%11%

This slab: GLOBAÏA's typology, in which filaments include walls seen edge-on. 3D: NEXUS+, Cautun et al. 2014.

A flattened view

The picture adds up or averages 10.5 megaparsecs of depth. A wall seen edge-on draws the same bright line as a filament, and a filament pointing at us looks like a round knot. Shape alone cannot settle it. Heat, X-rays and the microwave shadow help: hot ridges are more likely filaments, cool ones more likely walls, though that rule is an expectation and not a measured COLIBRE result.

The classes depend on the method

Twelve methods run on one simulated box agreed on the voids and on little else: the share of mass they put in filaments ranged from 11% to 62% (Libeskind et al. 2018). Even with full 3D information, a neural network trained to sort galaxies tells walls from filaments far less reliably than it spots voids (Inoue et al. 2022). The classes here are one careful reading, adapted to two dimensions, not a fact of nature.

The simulation

COLIBRE follows dark matter, gas, stars and black holes. The maps we received come from three boxes, 25, 200 and 400 megaparsecs wide, with gas allowed to cool far below ten thousand degrees. The coldest pixels here are the emptiest voids, where gas cools as it expands. This is the largest box, L400m7, seen at redshift 0.1. Each map pixel of the original is 3 kiloparsecs wide; the picture here is up to 4,096 pixels across.

Simulation: the COLIBRE collaboration (Schaye et al. 2025; Chaikin et al. 2025), maps provided by Rob McGibbon and the COLIBRE team. Colour schemes as on the COLIBRE website. Rendering, typology and close-ups: GLOBAÏA, October 2026.

Box sizes are comoving, as published: “Mpc/h” is a megaparsec scaled by little h (one megaparsec is about 3.26 million light-years). Particle counts are the resolution elements reported in each paper; hydrodynamical runs count dark matter and gas together.

Survey sky areas are in square degrees: the whole sky is about 41,253.

Images belong to the collaborations credited on each card and are shown here for education.

Simulated Universes is a GLOBAÏA project made for educational purposes only. It is not commercial and not a scientific product: for research, use the original data and papers credited on each card.