The Shapes of the Universe: From Spheres to Cosmic Filaments

Scientific Summary

The Universe organizes itself into three fundamental geometric shapes at different scales. The sphere (planets, stars) results from the isotropic balance between gravitation and internal pressure. The disk (spiral galaxies, protoplanetary disks) emerges from the conservation of angular momentum during gravitational collapse, creating a flat structure in equilibrium between gravity and centrifugal force. The filament network (cosmic web) is the largest-scale structure, formed by gravity amplifying primordial density fluctuations, with dark matter acting as a scaffold upon which baryonic matter aggregates into an interconnected network.

Why does the Universe exhibit shapes of spheres, disks, and filament networks?

Spheres, disks, and filaments are but the three faces of the same battle between gravity, pressure, rotation, and primordial structure, each shape corresponding to the scale and the mechanism that wins out. The Universe does not display these three major shapes by chance: each is the visible imprint of a dominant physical regime that imposes itself at a given scale. The sphere, that of stars and planets, is the shape of gravitational dominance over internal pressures. Gravity indeed acts isotropically: it compresses matter equally from all directions, hence a naturally round shape. Rotation can, however, deform it into a slightly flattened spheroid, called an oblate spheroid. The disk, observed in spiral galaxies or protoplanetary disks, is born from the conservation of angular momentum. When a cloud of matter collapses on itself, its rotation accelerates, exactly like an ice skater pulling in their arms. Matter is then projected towards an equatorial plane perpendicular to the rotation axis, while gravity and centrifugal force balance there to maintain a flat and stable structure. The filament network, which constitutes the cosmic web at the largest scale, is the signature of gravity acting on primordial density fluctuations. Originating from the Big Bang, these tiny variations are amplified by gravitational attraction over time. Dark matter, which represents about 85% of the total matter, plays the role of an invisible scaffolding here: it attracts ordinary matter, which then organizes into an immense network of filaments connected by nodes where galaxy clusters accumulate.

The Three Shapes of the Universe

The Universe, in its immensity and complexity, presents a structured organization that can be observed at different scales. From stars to the largest cosmic structures, three fundamental geometric shapes constantly emerge: the sphere, the disk, and the network of filaments. Each of these shapes reveals distinct physical processes and particular equilibria between the forces that govern the cosmos.

Overview of the shapes of the Universe

Why does the sphere appear in the Universe?

The natural symmetry of gravity

Geometric structures of the Universe
Structure	Shape	Predominant Force	Scale	Comment
Planet / star	Sphere	Gravitation ↔ Internal pressure	10⁶ – 10⁹ m	Gravitation balances with internal pressure, forming stable spheres.
Spiral galaxy	Disk	Rotation ↔ Gravitation	10²⁰ – 10²¹ m	Rotation and gravity produce flattened disks.
Cosmic filament	Filamentary network	Gravitation ⇒ large scale	10²³ – 10²⁵ m	Dark matter sculpts the filamentary network and gravitation amplifies anisotropies.

In the cosmic immensity, one geometric shape seems to dominate all others: the sphere. From stars to planets, through interstellar gas bubbles, this perfectly symmetrical shape appears as a constant across the scales of the Universe. This predominance is not a matter of chance, but the direct consequence of fundamental physical laws that govern our cosmos. The main reason for this spherical omnipresence lies in gravity. This fundamental force acts isotropically, meaning it exerts an equal attraction in all directions. When a sufficient amount of matter accumulates under its own gravity, it naturally tends to organize into a shape that minimizes its potential energy: the sphere. In this configuration, each particle is as close as possible to the collective center of mass, thus creating the most stable equilibrium.

An equilibrium between pressure and gravity

The sphere represents the perfect equilibrium shape between internal pressure and gravitational force. For celestial objects of significant size, their own gravity is strong enough to overcome the resistance of the materials they are made of, forcing them to adopt this quasi-spherical shape.

The effect of rotation

Another determining factor is rotation. Although gravity tends towards the perfect sphere, the rotation of celestial bodies introduces a flattening at the poles and a bulge at the equator. This is why some planets like Jupiter or Saturn are actually oblate spheroids rather than perfect spheres. However, the more massive an object is, the stronger its gravity and the more it resists this deformation, thus maintaining a shape closer to the ideal sphere.

Cosmic bubbles and uniform pressure

The same applies to gas bubbles in the interstellar medium, which take on this iconic spherical shape when subjected to uniform internal pressure.

A universal shape of equilibrium

The predominance of the sphere in the Universe reminds us that the shapes we observe are not arbitrary, but emerge directly from fundamental physical laws. From the birth of stars to the formation of planets, the sphere embodies equilibrium, stability, and energy efficiency that seem to be organizing principles of our Universe.

Why does the disk appear in the Universe?

The dynamics of angular momentum

If the sphere represents the shape of gravitational equilibrium, the disk embodies the rotational dynamics of the Universe. From spiral galaxies to forming planetary systems, this flat, circular shape emerges systematically wherever the conservation of angular momentum comes into play.

From gravitational collapse to flattening

The collapse of a gas and dust cloud into a disk is a direct consequence of the interaction between two fundamental physical principles: gravitation and the conservation of angular momentum. Initially, the cloud possesses a slight rotation, imperceptible but present (nothing is fixed in the Universe). Under its own gravity, the cloud begins to contract. This contraction is necessarily accompanied by an acceleration of its rotation, according to the same principle as an ice skater spinning faster when they pull their arms in towards their body.

N.B.:
An ice skater spins faster when pulling their arms in towards their body; this physical phenomenon illustrates the conservation of angular momentum. When the skater pulls in their arms, their moment of inertia \( I \) decreases, and to conserve the product \( L = I \omega \) (constant angular momentum), their angular velocity \( \omega \) increases.

An equilibrium between gravity and centrifugal force

Gravitational force acts spherically, attracting all matter towards the center. However, rotation generates a centrifugal force that opposes this attraction along the equatorial plane. Perpendicular to this plane, where the centrifugal force is zero, contraction proceeds freely. This difference in resistance to collapse depending on direction creates a progressive flattening.

Collisions and the formation of the common plane

Collisions between particles in the cloud dissipate energy but conserve the total angular momentum. Particles whose orbits are inclined eventually collide and transfer their motion, progressively aligning into a common plane. This flattening process leads to the formation of a thin, disk-like structure, where matter orbits the center of mass.

A universal pattern of structuring

This universal mechanism explains why we observe disks at all cosmic scales, from planetary systems forming around young stars to spiral galaxies like our Milky Way. The disk thus represents the dynamic equilibrium between gravitational contraction and rotation, a fundamental signature of physics in the Universe.

Why does a filament network appear in the Universe on a large scale?

The cosmic web: the largest structure in the Universe

The cosmic filament network, often described as the cosmic web, is the largest observable structure in the Universe. Its appearance results from the combined effect of gravitation and the initial conditions left by the Big Bang. The tiny density fluctuations present in the primordial Universe, revealed by the cosmic microwave background, served as seeds for this colossal structure.

From density fluctuations to gravitational structuring

Under the effect of gravity, regions slightly denser than average began to attract surrounding matter. This attraction preferentially acted along the axes of higher density, creating bridges of matter between the overdensities. Over billions of years, these bridges stretched and strengthened, forming the filaments we observe today.

The determining role of dark matter

Dark matter plays a fundamental role in this cosmic architecture. Representing about 85% of the total matter, it forms the gravitational scaffold upon which baryonic matter has accumulated. Its non-collisional nature allowed it to structure the Universe long before ordinary matter could.

The nodes of the web: birth of galaxy clusters

At the intersection of several filaments, where the gravitational field is most intense, galaxy clusters form: the largest coherent structures in the Universe. Between these dense nodes, filaments extend over hundreds of millions of light-years, while empty regions (called cosmic voids) separate this complex web.

A structure in permanent evolution

This filamentary structure is not static but evolves continuously. Under the effect of the accelerated expansion of the Universe, filaments stretch and distend, while new connections form between structures in formation. The cosmic web thus appears as the large-scale manifestation of the action of gravity over billions of years, sculpting the Universe from the initial tiny irregularities.

References

FAQ: Everything you need to know about the shapes of the Universe

Why is the sphere the dominant shape for stars and planets?

The sphere is the shape of minimal energy equilibrium under the effect of gravity. Gravitation acts isotropically (identically in all directions), pulling each particle towards the center of mass. For a given mass, the sphere minimizes the average distance between particles and the center, thus minimizing the gravitational potential energy. When a celestial object is massive enough, its own gravity overcomes the resistance of materials and forces it into a quasi-spherical shape. Rotation introduces a flattening (oblate spheroid), but the more massive the object, the more gravity resists this deformation.

How does a disk form from a rotating gas cloud?

The formation of a disk results from the interaction between gravitation and the conservation of angular momentum. A rotating gas cloud, collapsing under its own gravity, sees its rotation speed increase (skater effect: I↓ → ω↑). The centrifugal force opposes contraction in the equatorial plane, but perpendicular to this plane, where this force is zero, contraction proceeds freely. Collisions between particles dissipate energy and progressively align orbits into a common plane. This results in a flat and circular structure, the disk, in equilibrium between gravitational attraction towards the center and the centrifugal force due to rotation.

What is the "cosmic web" and how did it form?

The cosmic web is the largest structure in the Universe, a network of filaments of matter (galaxies, gas, dark matter) extending over hundreds of millions of light-years, separated by vast voids. It was born from primordial density fluctuations (tiny variations in density after the Big Bang, visible in the cosmic microwave background). Gravity amplified these overdensities: denser regions attracted surrounding matter, preferentially along the axes of higher density, forming filaments. Dark matter (~85% of matter) played the role of a gravitational scaffold by structuring first, with baryonic matter accumulating on it later. Galaxy clusters, the densest nodes of the web, form at the intersections of filaments.