Anisotropies and Inhomogeneities
Linas JuozėnasShare
Knowledge Ark · Universe · Chapter 10 / Article 09
An almost smooth beginning. A universe of structure.
Why is the universe filled with galaxies, filaments, and enormous voids if it began so nearly uniform? Small differences—and the way they change with scale and time—connect these two pictures.
What the differences reveal
A map of galaxies looks anything but smooth. Some regions contain crowded clusters; others stretch across vast, sparsely populated spaces. Yet cosmologists describe the universe with a model whose large-scale background is homogeneous and isotropic.
Those statements address different levels of description. To understand how they fit together, we need to distinguish direction from position, a local feature from a statistical pattern, and an observation from the physical model used to explain it.
Two words for different kinds of variation
Anisotropy means that a property depends on direction. A sky map with warmer microwave radiation in some directions than others contains temperature anisotropies. Inhomogeneity means that a property varies from place to place: matter density differs between a galaxy cluster and a neighboring void.[2]
The distinction matters. Imagine an observer at the center of concentric shells whose density changes with radius. Every direction could look the same, even though density changes with position. Inferring homogeneity therefore requires more than an isotropic view from one location. The Copernican principle—that our location is not specially privileged—is an additional assumption that cosmologists seek to test.[3]
How can a clumpy universe be broadly uniform?
Statistical homogeneity means that the statistical description does not depend on where a region is placed. Statistical isotropy means it does not depend on orientation. Neither requires every region to contain identical galaxies. In the standard cosmological picture, averaging over larger volumes makes local density contrasts less prominent, with a gradual approach toward large-scale uniformity.[2]
One observational test counts galaxies inside spheres of increasing radius. In a homogeneous distribution, the mean count approaches growth proportional to volume: N(<r) ∝ r³. The WiggleZ survey tested this approach with an explicit tolerance and corrections for survey selection. A quoted “homogeneity scale” therefore depends on the chosen criterion, sample, and analysis; it is not a universal boundary beyond which all structure disappears.[2]
Smoothing a picture is not a proof. Averaging reduces fine detail by construction. A scientific test must compare measurements with quantitative predictions and check what the survey could have detected.
How do we describe the strength of a fluctuation?
δ = (ρ − ρ̄) / ρ̄
The density contrast, δ, compares local density ρ with the mean ρ̄ at the same cosmic time. Positive values indicate an overdensity; negative values indicate an underdensity. A region with twice the mean density has δ = 1. One with half the mean has δ = −0.5.[4]
The next question is how these differences are arranged. A two-point correlation function measures whether pairs of galaxies occur more often at a particular separation than expected from an unclustered reference sample. The power spectrum, P(k), expresses related information by separating the pattern into contributions from different spatial wavelengths. Large k corresponds to small spatial scales.[5]
On the sky, the angular power spectrum, Cℓ, describes fluctuation strength at different angular scales. Low ℓ represents broad patterns; high ℓ represents finer detail. These statistics let researchers compare observations with predictions without expecting a simulation to place every individual galaxy or hot patch exactly where we observe it.[6]
What CMB anisotropies actually show
The cosmic microwave background, or CMB, is nearly uniform radiation left from the early universe. Its prominent dipole—a warmer half of the sky opposite a cooler half—is dominated by our motion relative to that radiation. Researchers remove this contribution, whose amplitude is about 3.36 millikelvins, and separate foreground emission before studying the much smaller cosmological pattern.[7]
The remaining temperature fluctuations have a characteristic scale of tens of microkelvins, roughly one part in 100,000 of the mean temperature, with amplitude depending on angular scale. They combine intrinsic temperature differences, gravitational redshifts, plasma motions, and effects accumulated along the light’s journey. A hot patch is therefore not a direct label for a denser patch of matter.[6]
Before photons decoupled, gravity and radiation pressure drove oscillations in the coupled photon–baryon plasma. Their imprint produces the CMB’s acoustic peaks. The peaks’ relative strengths and spacing help constrain the plasma’s composition and the cosmological geometry connecting physical scales to observed angles.[8]
Polarization adds another pattern
Scattering by electrons produces linear polarization when the incoming radiation has the required directional variation. E modes and B modes describe the geometry of that polarization pattern across the sky. They are not maps of separate cosmic electric and magnetic fields.[9]
Two origins of B modes
Gravitational lensing converts part of the E-mode pattern into B modes, and that signal has been observed.[10]
A separate contribution from primordial gravitational waves remains unconfirmed. Its detection would test early-universe physics; existing upper limits constrain models without establishing a unique origin of the fluctuations.[11]
How structure grows
Inflation offers a leading explanation for the initial seeds. In many inflationary models, quantum fluctuations become primordial perturbations during an early period of accelerated expansion. Observations favor a nearly scale-invariant primordial curvature spectrum—roughly similar fluctuation power per logarithmic range of wavelength. They also favor predominantly adiabatic perturbations, which initially preserve relative particle abundances, such as the number of baryons per photon. These successes support inflationary models, while leaving the mechanism and a unique inflationary origin unestablished.[12]
Dark matter perturbations were already evolving before recombination. Growth was suppressed during radiation domination and became more effective as matter came to dominate. Later, overdense regions could become strongly nonlinear: their evolution could no longer be described as a small correction to a smooth background. Halos assembled through accretion and mergers, while gas cooling and stellar feedback helped determine which galaxies formed inside them.[1]
Underdense regions evolved too. Matter tended to flow outward relative to the average expansion, leaving voids increasingly sparse. Voids still contain matter, galaxies, and faint internal structure. Their surroundings can also deform them or squeeze smaller voids out of existence.[13]
The resulting cosmic web is the later chapter of the fluctuation story. The nearly smooth early universe and the clustered universe seen in galaxy surveys belong to different stages of its evolution.
What telescopes measure—and what models infer
| Probe | Measured pattern | What it helps infer |
|---|---|---|
| CMB | Temperature and polarization across the sky. | Primordial conditions and the physical processes that shaped the radiation pattern.[12] |
| Galaxy surveys | Sky positions and redshifts of selected galaxies. | Clustering and its evolution, after accounting for how galaxies trace matter.[4] |
| Weak lensing | Small, correlated distortions in many background-galaxy shapes. | The intervening matter distribution through its integrated effect on light.[14] |
A galaxy map is not an exact matter map. Galaxy bias describes the physical relationship between a galaxy population and the underlying matter distribution. Different populations can cluster differently because their formation histories and environments differ. This must be modeled when using galaxies to infer matter fluctuations.[4]
Nor is a deep survey a simultaneous photograph of today’s universe. More distant objects are generally seen at earlier stages. Realistic comparisons build a lightcone from different simulated epochs to match the times sampled by the observations.[15]
Apparent patterns can also come from the observing process. A deeper exposure finds fainter galaxies; dust or instrument effects can reduce counts elsewhere. Teams model survey selection and compare clustering with random catalogs that reproduce the observing coverage without adding a physical clustering signal. Simulated observations help test whether the analysis recovers the intended information.[5]
For weak lensing, telescope blurring, uncertain source distances, overlapping images, and naturally aligned galaxy shapes can mimic or alter the signal. Gas physics also changes the predicted matter distribution on small scales. Averaging more galaxies reduces random noise but does not automatically remove these biases.[16]
Testing gravity, particles, and the earliest seeds
Expansion and growth are connected. Within general relativity, a specified matter content and expansion history predict how small matter fluctuations grow. The later influence of dark energy suppresses growth relative to continued matter domination. Comparing measured expansion with measured clustering therefore tests this relationship; alternative gravity theories can change it.[17]
Neutrinos leave a scale-dependent effect. Because relic neutrinos move rapidly, they cluster less efficiently than cold dark matter on sufficiently small scales and reduce the growth of structure there. The relevant scales depend on neutrino mass and cosmic epoch. Cosmological mass constraints consequently require a model; they are not a direct weighing of individual particles.[18]
Primordial non-Gaussianity concerns correlations beyond those described by a Gaussian random field. Searches test several possible patterns, each with its own sensitivity and limits. Planck’s analyses found no significant primordial signal among the tested templates. A single universal bound on “non-Gaussianity” would hide those differences.[19]
Later complexity does not by itself reveal exotic initial conditions. Nonlinear gravity and the way galaxies form generate higher-order correlations even from Gaussian beginnings. Researchers must separate these later contributions from any primordial signature.[20]
When does an anomaly become evidence?
Some broad CMB features—including the Cold Spot, unusually low large-angle correlations, and differences between hemispheres—remain subjects of study. Their presence in maps is distinct from their significance as evidence against the standard model. Testing many directions, smoothing scales, or statistics after inspecting a map can make an unusual-looking result seem more surprising than it is.[21]
There is also cosmic variance: we observe one realization of the universe. The largest angular patterns contain relatively few independent modes, so even a perfect instrument would leave statistical uncertainty. Better temperature measurements do not provide a second independent sky, although polarization adds information.[21]
Comparisons of late-time clustering require similar care. The common parameter S₈ combines the fluctuation amplitude σ₈ with matter density. It depends on calibration and the fitted cosmological model. The 2025 KiDS-Legacy weak-lensing analysis found its baseline S₈ consistent with Planck, illustrating why it is inaccurate to say that all lensing surveys find a universe that is “too smooth.”[22]
How are σ₈, S₈, and H₀ different?
σ₈ is the root-mean-square linear-theory matter-density contrast at the present epoch, after averaging in comoving spheres of radius 8 h⁻¹ Mpc, where h = H₀/(100 km/s/Mpc). S₈ = σ₈√(Ωm/0.3) is a commonly used combination with the present matter-density fraction Ωm. H₀ is today’s expansion rate. Their inferred values can be related through a model, but the Hubble tension is not itself a measurement of clustering strength.[17]
What would strengthen the evidence?
Progress depends on comparing observations with different sensitivities. Galaxy clustering traces where selected objects lie; lensing responds to intervening matter; the CMB constrains early conditions. A model that fits their combination faces a more demanding test than one fitted to a single dataset.[17]
That requires better observations and better control of the comparison: representative calibration samples, realistic synthetic surveys, and predictions tested beyond the data used to tune them.[15], [16] A convincing new effect should survive changes in instruments, sample selection, and analysis choices.
The pattern is part of the evidence.
Small variations in ancient light, dense knots of galaxies, and sparse cosmic voids offer connected ways to investigate cosmic history. Learning to read those differences means asking what varies, on which scale, at what time—and how reliably we can measure it.
Continue with Current Debates and Outstanding Questions to explore where these tests leave cosmology’s most persistent puzzles.
Sources and further reading
Original research, scientific reviews, and official survey information. Checked in September 2026. The original illustrations explain concepts; they are not observations or cosmological simulation results. The smoothing demonstration uses one constructed field and a fixed color scale.
- Frenk & White (2012) — Dark matter and cosmic structureCold dark matter, radiation-era growth suppression, halo assembly, and the separate physics of galaxy formation.
- Scrimgeour et al. (2012) — The WiggleZ Survey: Transition to Large-Scale Cosmic HomogeneityTests homogeneity through galaxy counts, with an explicit tolerance and survey corrections.
- Clarkson & Maartens (2010) — Inhomogeneity and the Foundations of Concordance CosmologyDistinguishes directional isotropy from spatial homogeneity and explains what can be inferred from one observer’s sky.
- Desjacques, Jeong & Schmidt (2018) — Large-Scale Galaxy BiasDensity statistics and the physical relation between galaxy clustering and the underlying matter.
- DESI Collaboration (2025) — DESI 2024 II: Sample Definitions, Characteristics, and Two-point Clustering StatisticsSurvey selection, random catalogs, instrument corrections, and validation with simulated observations.
- Wands, Piattella & Casarini (2016) — Physics of CMB radiationTemperature contributions, angular statistics and the limits imposed by observing one sky.
- Planck Collaboration (2018/2020) — Overview and Cosmological LegacyDistinguishes the dominant motion-induced dipole from the much smaller cosmological temperature pattern.
- Hu & Dodelson (2002) — Cosmic microwave background anisotropiesGravity, radiation pressure, baryon loading and the damping of small-scale acoustic structure.
- Hu & White (1997) — A CMB Polarization PrimerThomson scattering, quadrupoles, and the geometry of E- and B-mode polarization.
- Hanson et al. (2013) — Detection of Lensing B Modes with the South Pole TelescopeSPTpol reported the first detection of gravitational-lensing B-mode polarization in 2013.
- Balkenhol et al. (2026) — Inflation Constraints from Combined CMB and BAO DataCombined CMB data constrain primordial tensors; the limit depends on datasets, pivot, and tensor-spectrum assumptions.
- Planck Collaboration (2018/2020) — Constraints on InflationTests the primordial perturbation spectrum and inflationary models without identifying a unique origin.
- van de Weygaert & Platen (2009) — Cosmic Voids: Structure, Dynamics and GalaxiesVoids contain matter and galaxies, preserve faint substructure, and evolve through expansion, merging and environmental squeezing.
- Bartelmann & Schneider (2001), Weak Gravitational LensingStatistical shape distortions constrain the matter encountered by light along its path.
- Overzier et al. — The Millennium Run Observatory: First LightWhy realistic mock surveys sample galaxies at different cosmic times along the observer’s lightcone.
- Mandelbaum (2018), Weak Lensing for Precision CosmologyExplains the calibration and astrophysics needed to interpret weak-lensing patterns.
- Weinberg et al. (2013) — Observational Probes of Cosmic AccelerationCombining expansion and structure-growth measurements tests cosmology more fully than either measurement alone.
- Lesgourgues & Pastor (2012) — Neutrino Mass from CosmologyNeutrino free streaming changes clustering on scales that depend on particle mass and cosmic epoch.
- Planck Collaboration (2019) — Constraints on Primordial Non-GaussianityNon-Gaussianity tests depend on the correlation pattern being tested; there is no single universal fNL limit.
- Jeong & Komatsu (2009) — Primordial Non-Gaussianity and the Galaxy BispectrumGravitational evolution and galaxy bias create higher-order correlations even from Gaussian initial fluctuations.
- Planck Collaboration (2020) — Planck 2018 Isotropy and Statistics of the CMBLarge-angle features are real features of the maps; their significance as departures from cosmological isotropy remains uncertain.
- Wright et al. (2025) — KiDS-Legacy Cosmic-Shear ConstraintsA recent weak-lensing analysis shows why calibration and parameter definitions matter in comparisons of clustering strength.
Cosmology and the Universe’s Large-Scale Structure
- Cosmic Inflation: Theory and Evidence
- The Cosmic Web: Filaments, Voids, and Superclusters
- The Cosmic Microwave Background’s Detailed Structure
- Baryon Acoustic Oscillations
- Redshift Surveys and Mapping the Universe
- Gravitational Lensing: A Natural Cosmic Telescope
- Measuring the Hubble Constant: The Tension
- Dark Energy Surveys
- Anisotropies and Inhomogeneities · You are here
- Current Debates and Outstanding Questions