Cosmic Voids

The universe is mostly empty bubbles

Plot the positions of a million galaxies in three dimensions and you do not get a uniform fog. You get a sponge. Galaxies trace bright, thread-like filaments that meet at dense nodes — the galaxy clusters — and drape into two-dimensional walls. In between, occupying most of the picture, are the dark interiors: the cosmic voids. They are the holes in the sponge. A single large void can be 100 million to half a billion light-years across and contain only a handful of galaxies where hundreds would sit if matter were spread evenly.

The striking fact is that voids dominate the volume of the cosmos while holding almost none of its mass. Depending on how you draw the boundaries, voids fill on the order of 60% of space yet contain a small minority of the galaxies. The universe, structurally, is closer to foam than to soup: thin films of matter wrapped around enormous bubbles of near-emptiness. Cosmic voids are those bubbles.

They are not accidents or gaps in the data. Voids are a direct, predictable consequence of how gravity sculpts an almost-uniform early universe over 13.8 billion years — and because they are the places where gravity has the least to work with, they are where the smooth, repulsive influence of dark energy shows up most clearly.

How a void grows: gravity runs in reverse

The early universe was astonishingly smooth — the cosmic microwave background tells us density fluctuations were only about 1 part in 100,000 at recombination. But those tiny ripples carried both crests (slightly overdense) and troughs (slightly underdense). Gravity is an amplifier of contrast. Overdense regions pull in more matter and grow denser; underdense regions, having less than their share of gravity, lose the tug-of-war and are progressively emptied as their matter drains onto the surrounding structures.

An underdense patch therefore behaves like a small, self-contained open universe embedded in the larger one. With sub-average density it decelerates less, so it expands faster than the cosmic mean. In comoving coordinates — coordinates that factor out the overall expansion — the void literally grows: matter flows outward from its centre toward the walls. The outflow at the edge of a large void reaches a few hundred kilometres per second, a coherent peculiar velocity superimposed on the Hubble flow.

Crucially, voids tend to become more spherical as they evolve, because the outflow is fastest along the shortest axis. Small voids that find themselves inside a larger underdensity get squeezed out of existence — this void-in-void and void-in-cloud hierarchy was worked out by Sheth and van de Weygaert (2004) and explains why the void size function turns over: tiny voids are continually erased, leaving a characteristic large-void population.

The math of an emptying region

The natural variable is the dimensionless density contrast,

δ(x) = [ρ(x) − ρ̄] / ρ̄

where ρ̄ is the mean cosmic matter density. A void has δ < 0, and a deep void interior reaches δ ≈ −0.8 (only 20% of mean density). The lowest physically possible value is δ = −1, a true vacuum, which voids approach but never reach.

In linear theory, density perturbations grow in lockstep with the linear growth factor D(a): δ(a) = D(a) δ₀. But voids quickly leave the linear regime, and the clean nonlinear result is that a region evolving toward emptiness asymptotically reaches a linear-theory density contrast at shell-crossing of

δ_v ≈ −2.71   (linearly extrapolated, top-hat void)

This is the void counterpart of the famous δ_c ≈ 1.686 collapse threshold for clusters. It is the number that goes into excursion-set predictions of how many voids of each size should exist. The mass conservation behind void expansion is just continuity: as the comoving radius of the void's edge grows, the same outflowing matter piles up into the surrounding wall, so a ridge of slight overdensity always rims a void.

The expansion excess can be summarised with a local effective Hubble rate. For a spherical underdensity the radial outflow velocity at the void edge of comoving radius R is approximately

v_out ≈ −(1/3) H R f δ̄(R)

where f = dlnD/dlna ≈ Ω_m^0.55 is the linear growth rate and δ̄(R) is the mean enclosed contrast (negative for a void, so v_out points outward). Because f depends on Ω_m and on the theory of gravity, this outflow is a direct probe of both.

How we actually find them

Voids are defined by what is missing, which makes detection an exercise in mapping absence. There is no single agreed definition, so several algorithmic families coexist:

• Watershed / Voronoi finders (ZOBOV, VIDE). Tessellate space with a Voronoi cell around each galaxy. A galaxy in a sparse region owns a large cell; the algorithm then runs a watershed flood from each local density minimum, merging basins into voids. No assumption about void shape is needed, which is why ZOBOV/VIDE became the community standard for SDSS, BOSS and DESI catalogues.
• Sphere-growing finders. Inflate an empty sphere from a candidate centre until it touches a tracer galaxy; the largest such spheres define voids. Simple and shape-restrictive, but fast and easy to interpret.
• Dynamical / phase-space finders. Classify each point by the number of axes along which matter is collapsing (the cosmic-web "T-web" or "V-web"). Voids are regions collapsing along zero axes — expanding in all three.

The practical catch is shot noise: a void's depth depends on how densely you sample it with tracer galaxies. A survey that sees only the brightest galaxies will overstate void emptiness, because the faint galaxies that do live inside are invisible. Modern analyses calibrate against mock catalogues built from N-body simulations to correct for this tracer bias.

Sizes, densities and timescales — the numbers

Quantity	Typical value	Notes
Effective radius	10 – 50 Mpc	Most catalogued voids; largest reach ~100 Mpc
Diameter	~65 – 650 million ly	1 Mpc ≈ 3.26 million ly
Interior contrast δ	−0.6 to −0.9	Deepest centres approach δ ≈ −0.95
Linear void threshold δ_v	≈ −2.71	Shell-crossing, top-hat model
Volume fraction of space	~60 %	Definition-dependent; voids dominate by volume
Edge outflow velocity	~100 – 400 km/s	Peculiar velocity on top of Hubble flow
Wall overdensity (rim)	δ ~ +1 to +5	Evacuated matter piles onto the boundary
ISW temperature dip	~ few μK	Stacked CMB signal along void lines of sight

For scale: the observable universe is about 28,000 Mpc across, so a 100 Mpc void is roughly 0.4% of the cosmic horizon in each dimension — small on the largest scales, but staggering compared with the ~30 Mpc separation between major galaxy clusters. A void is bigger than the gulf between superclusters.

Worked example: how empty is the Boötes void?

The Boötes void, discovered in 1981 by Robert Kirshner, Augustus Oemler, Paul Schechter and Stephen Shectman, is the textbook case. Take a representative radius R ≈ 60 Mpc (it is often quoted as 100–150 Mpc in diameter). How many galaxies should live inside, and how many do we see?

The mean number density of bright galaxies in the universe is roughly n̄ ≈ 0.01 per Mpc³ (down to a useful luminosity limit). The volume of the void is

V = (4/3) π R³
  = (4/3) π (60 Mpc)³
  ≈ 9.0 × 10⁵ Mpc³

so the expected count at mean density is

N_expected = n̄ V ≈ 0.01 × 9.0 × 10⁵ ≈ 9,000 galaxies

Surveys instead find only a few dozen galaxies inside the Boötes void's main volume — roughly 60. The interior density contrast is therefore

1 + δ = N_observed / N_expected ≈ 60 / 9,000 ≈ 0.007
δ ≈ −0.99

So in luminous galaxies the void looks nearly empty. The dark-matter contrast is shallower — closer to δ ≈ −0.8 — because galaxy formation is biased: galaxies preferentially light up only where the dark matter is densest, so the absence of galaxies exaggerates the absence of mass. This galaxy bias is exactly why void cosmology must be calibrated with simulations rather than read off naïvely from galaxy counts.

Why cosmologists love voids: a dark-energy laboratory

In a cluster, self-gravity dominates and dark energy is a small correction. In a void it is the reverse: there is so little matter that the smooth dark-energy component governs the dynamics. That makes voids unusually clean places to test the nature of cosmic acceleration. Three probes stand out:

• Integrated Sachs-Wolfe (ISW) effect. An underdensity is a gravitational potential hill, not a well. A CMB photon entering a void must climb that hill, losing a little energy, then regains it on the way down. In a matter-only universe the hill is static and the energy is returned exactly. But with dark energy stretching the void while the photon is inside, the hill flattens during the crossing — the photon descends a smaller hill than it climbed, so the gain no longer cancels the loss and it emerges slightly cooler. Stacking the CMB along thousands of void sightlines reveals a coherent cold dip of a few microkelvin — direct evidence that the potentials are decaying, i.e. that dark energy is real.
• Alcock-Paczyński (AP) test. Voids are statistically spherical on average. If we assume the wrong cosmology when converting redshifts and angles to distances, spheres come out as ellipsoids. Measuring the apparent flattening of stacked voids therefore pins down the geometric quantity H(z)·D_A(z), constraining the dark-energy equation of state w.
• Void lensing and abundance. An underdensity is a diverging lens: it de-magnifies and tangentially distorts background galaxies, giving a weak-lensing signal opposite in sign to a cluster. And because the void size function depends on the growth rate of structure, simply counting voids of each size constrains modified-gravity theories, which often boost growth in low-density regions where screening mechanisms switch off.

The DESI and Euclid surveys are mapping tens of thousands of voids precisely to drive these tests, with the AP and ISW measurements expected to deliver percent-level constraints on w.

Famous voids and the structures around us

• The Boötes void. The original "great void," ~100–150 Mpc across in the direction of the constellation Boötes. Its discovery in 1981 forced cosmologists to take large-scale structure seriously as a quantitative subject.
• The Local Void. A modest void bordering our own Local Group, at least ~45 Mpc across. The Milky Way sits on its edge, and the void is actively pushing our galaxy away from it at hundreds of km/s — a measurable contributor to the Local Group's peculiar motion.
• The KBC void (Keenan-Barger-Cowie). A large, shallow local underdensity, perhaps ~300 Mpc in radius with δ ≈ −0.2, in which the Milky Way appears to be embedded. It has been proposed as a partial explanation for the Hubble tension — local expansion measured inside an underdensity would run a few percent fast — though the effect is too small to resolve the full tension.
• The Eridanus supervoid / CMB Cold Spot. The most prominent cold anomaly in the CMB lies toward Eridanus, and a supervoid hundreds of Mpc across has been proposed along that line of sight to explain it via an enhanced ISW signal. Its reality and adequacy remain genuinely debated.
• Survey void catalogues. SDSS, BOSS, and now DESI have catalogued thousands of voids; the VIDE and REVOLVER public catalogues are the workhorses for void cosmology, spanning effective radii from ~10 to ~100 Mpc out to redshift z ~ 1.

Voids vs other "empty" structures

The word "void" gets attached to several different things on different scales. They are not the same.

Structure	Scale	What is missing	Density contrast
Cosmic void	10 – 100+ Mpc	Galaxies, dark matter, gas	δ ≈ −0.8
Supervoid	100 – 300+ Mpc	Whole superclusters' worth of galaxies	δ ≈ −0.1 to −0.3 (shallow)
Intergalactic medium	filling all space	nothing — it is the baseline gas	δ ≈ 0 to a few
Local Bubble (interstellar)	~100 pc	interstellar gas, within our Galaxy	not cosmological
Bok globule / cloud cavity	sub-pc to pc	blown-out gas, stellar feedback	not cosmological

The key distinction: a cosmic void is a cosmological underdensity in the matter distribution, sculpted by gravity over Gyr timescales. A supervoid is just a very large, typically shallow cosmic void. The "voids" inside galaxies — the Local Bubble, gas cavities cleared by supernovae — are parsec-scale interstellar features and have nothing to do with large-scale structure beyond sharing the name.

Common misconceptions and edge cases

• "Voids are completely empty." No. A void interior still holds ~10–20% of mean density in dark matter and gas, plus a sparse, distinctive galaxy population. The deepest centres approach but never reach δ = −1.
• "A void is just a region with no galaxies." Defining voids purely by galaxy absence is dangerous, because galaxy bias makes the void look emptier than the underlying mass field. The actual matter underdensity is always shallower than the galaxy underdensity.
• "Voids are static holes." They are dynamic and growing. Matter streams out of their interiors at hundreds of km/s, walls thicken, and small voids inside larger ones get crushed out of existence (void-in-cloud collapse).
• "Voids expand because space inside them is different." The dark energy density is the same everywhere; what differs is that voids have so little matter that dark energy dominates locally, so the relative expansion is faster. There is no exotic physics inside a void — just an unusually favourable balance for the cosmic-average repulsion.
• "The void shape tells you the cosmology directly." Only statistically. Any single void is triaxial and noisy; the Alcock-Paczyński test works on the stacked, averaged shape of many voids, which is spherical by symmetry, not on any individual one.
• "A big enough local void explains the Hubble tension." A local underdensity like the KBC void does bias local H₀ measurements slightly high, but the magnitude is at most ~1–2%, well short of the ~9% needed to reconcile the local and CMB values. It is a contributor, not a cure.