Redshift Surveys and Mapping the Universe
Linas JuozėnasShare
Knowledge Ark · Universe · Chapter 10 / Article 05
A sky of points. A universe in depth.
Two galaxies can appear side by side while lying enormously far apart. By reading the wavelengths of their light, astronomers turn a flat view of the sky into a map with depth—and a record of cosmic history.
What lies behind the pattern on the sky?
A photograph gives us directions, brightnesses, and shapes. It does not immediately tell us which galaxies are neighbors, which belong to a distant cluster, or which merely overlap in our view. Redshift surveys add the information needed to begin separating those possibilities.
The result is cosmic cartography: a way to study walls, filaments, and voids, compare galaxy populations across time, and test the physics driving expansion and structure growth. Reading these maps well means understanding both the universe and the way a survey observes it.
How do we measure a galaxy’s redshift?
A spectrum separates light by wavelength. Emission and absorption features form recognizable patterns that can be compared with rest-frame templates. Survey pipelines search for the redshift that best matches the observed spectrum, using the overall pattern and fit quality to distinguish reliable measurements from ambiguous ones.[2]
1 + z = λobserved / λrest
Redshift z measures the fractional change in wavelength. For example, 500 nanometers observed at 750 nanometers gives z = 0.5.[3]
For light traveling between observers following the average cosmic expansion, 1 + z = anow/aemitted, where a is the cosmic scale factor. With anow set to one, z = 1 corresponds to emission when that scale factor was one-half. A galaxy’s observed redshift can also include motion relative to the average expansion.[3]
How does redshift become distance?
At sufficiently low redshift, the smooth Hubble flow gives the useful approximation d ≈ cz/H₀, where c is the speed of light and H₀ the present expansion rate. Nearby galaxy motions can be a substantial fraction of that signal, however. Simply treating cz as a recession speed is not an accurate general rule for distant objects.[4]
At larger redshifts, astronomers calculate distance using a specified expansion history. One common choice is line-of-sight comoving distance, which factors out the overall expansion so that structures at different epochs can be compared using consistent coordinates.[3]
The distance calculation
DC(z) = c ∫0z dz′/H(z′). Here H(z′) is the expansion rate at redshift z′. The calculation depends on the cosmological model. Comoving distance is distinct from angular diameter distance and light-travel time.[3]
A map assembled from different times
The light from a more distant galaxy generally began its journey earlier. A survey therefore samples our past light cone: different regions appear at different stages of their history. It is not a simultaneous photograph of the whole universe as it exists today. Realistic simulated surveys account for this by selecting galaxies at the appropriate evolutionary stage along the light cone.[5]
The direct observations are sky position and redshift. Converting them into a map in megaparsecs adds a cosmological model. Testing that model remains part of the science.
Which surveys transformed cosmic cartography?
1986: a revealing CfA slice
De Lapparent, Geller, and Huchra’s “A Slice of the Universe” presented a narrow redshift wedge from the extended CfA survey. Concentrations and large underdense regions became much clearer when depth was added to the sky projection.[1]
1989: the Great Wall
Geller and Huchra subsequently described the Great Wall, an immense sheet-like concentration of galaxies. This was a separate report from the 1986 slice. Some structures reached the survey boundaries, illustrating how the size of a map limits what can be measured.[6]
2dF: spectroscopy on a much larger scale
The 2dF Galaxy Redshift Survey released 221,414 reliable galaxy redshifts in its 2003 final catalog.[7] In 2005, Cole and colleagues analyzed its power spectrum and found evidence for baryon acoustic oscillations. That result complemented the acoustic peak measured in SDSS’s correlation function.[8]
SDSS, BOSS, and eBOSS: connecting cosmic epochs
The Sloan Digital Sky Survey developed an extensive legacy of imaging and spectroscopy. BOSS greatly expanded galaxy and quasar samples, while eBOSS extended their cosmological reach. The programs also used the Lyman-alpha forest: intervening hydrogen absorption in distant quasar spectra, which traces structure beyond much of the galaxy sample.[9]
These maps became more than catalogs. Researchers could measure clustering and its directional patterns across redshift, connecting the distribution of galaxies to cosmic expansion and the growth of structure.[9]
What appears when the map gains depth?
Galaxies gather into groups and clusters, stretch along filaments and sheets, and surround underdense regions. In the standard cosmological picture, this cosmic web grows as gravity amplifies initial matter-density fluctuations. Dark matter supplies much of the gravitational structure, while gas cooling and star formation determine where luminous galaxies appear.[10]
Voids contain structure too
A void is underdense, not empty. It can contain galaxies, small halos, and a faint internal network. Its boundary and measured size depend on the tracer population and the method used to identify it.[11]
Large does not always mean bound
A named supercluster can join several concentrations across an enormous region. That label does not automatically mean the whole region is gravitationally bound or has settled into equilibrium. Its denser parts may have a different future from its outskirts.[12]
To move beyond visual impressions, astronomers measure statistics. The two-point correlation function describes the excess probability of galaxy pairs at a given separation; the power spectrum describes clustering by spatial scale. These related views allow data and cosmological predictions to be compared quantitatively.[13]
Why do some structures look stretched or squashed?
Peculiar velocity means motion relative to the average cosmic expansion. Its line-of-sight component changes a galaxy’s measured redshift. If every shift is interpreted as distance, that motion displaces the galaxy’s apparent radial position in the map.[4]
Within clusters, random orbital velocities create apparent radial elongations called Fingers of God. On larger scales, coherent infall produces a statistical flattening along the line of sight, commonly called the Kaiser effect. Both arise from velocities, but in different dynamical regimes.[14]
A separate distortion appears if the assumed cosmology converts angular and redshift intervals with the wrong relative scales. This is the basis of the Alcock–Paczyński test. Because geometry and peculiar velocities both alter apparent directional patterns, analyses must model their effects together.[15]
How do expansion and peculiar redshift combine?
Ignoring smaller gravitational contributions and after correcting the observer’s motion, 1 + zobserved = (1 + zcosmic)(1 + zpeculiar). The shifts multiply; simply subtracting cz − H₀d is only a low-redshift approximation.[4]
What makes a survey trustworthy?
A survey has limits: sky coverage, brightness thresholds, target colors, observing conditions, and the probability of obtaining a reliable redshift. Together these define its selection function. A thinning galaxy sample at greater distance might reflect missed faint objects rather than a physical decline in density.[16]
Researchers model these effects with completeness weights and random catalogs that follow the observing pattern without physical clustering. Mock surveys add simulated structure and observational limitations, helping test recovery of the intended signal and estimate correlated uncertainties. Such corrections must be validated; their existence does not guarantee that every bias is removed.[16]
Spectroscopic and photometric redshifts serve different needs
| Method | Information used | Main trade-off |
|---|---|---|
| Spectroscopic | Resolved spectral features or a fitted spectrum | Usually sharper radial positions, with more observing effort per source |
| Photometric | Brightnesses through several filters | Very large samples, usually with broader and sometimes ambiguous redshift estimates |
Precision depends on the source, signal quality, filters, and method. Neither approach has one universal redshift error.[17]
Photometric analyses often work with redshift probability distributions rather than a single exact value. Representative spectroscopy and cross-correlations with reference samples help calibrate their population distributions. Calibration must account for differences between the reference sample and the galaxies being studied.[17]
There is also galaxy bias: a selected galaxy population does not trace total matter perfectly. Different galaxy types occupy different environments, so their clustering need not have the same amplitude. Large-scale bias models are useful approximations; smaller-scale and precision analyses require richer treatment.[18]
What can these maps tell us about cosmology?
An acoustic ruler measures expansion
Baryon acoustic oscillations leave a weak statistical feature near a roughly 150-megaparsec comoving scale. Across the sky, it constrains transverse distance relative to the ruler; along the line of sight, it constrains the expansion rate multiplied by the ruler. Measurements at several redshifts trace how cosmic geometry changes with epoch.[19]
Converting those ratios into an absolute scale requires calibration. BAO alone does not independently determine H₀; its interpretation depends on the sound horizon and the assumed early physics. Comparisons with CMB and supernova measurements therefore test both the expansion history and the consistency of the calibration chains.[20]
Directional clustering measures growth
Redshift-space distortions contain information about how rapidly structure grows. A commonly reported combination, fσ₈, links the growth rate to the amplitude of matter fluctuations. Extracting it requires a model connecting galaxy density and velocity to the underlying matter field. It is not a direct measurement of gravity without assumptions.[21]
Using more of the clustering pattern—its full shape—adds sensitivity to matter density, fluctuation amplitude, and other cosmological ingredients. For example, DESI’s first-year full-shape analysis combined these measurements with acoustic information and additional data. Its constraints depend on the model and on which observations are included.[13]
Current hints still need cross-checks
Some joint analyses prefer evolving dark energy over a cosmological constant, with strength that varies by model and dataset. DESI’s 2026 analysis of DR2 Lyman-alpha geometry slightly reduced the discrepancy with CMB expectations. A larger map does not necessarily strengthen a previous hint, and these results do not establish dark energy’s physical identity.[22]
What else can we learn from the same observations?
Mapping flows needs another distance measurement
To estimate an individual galaxy’s peculiar velocity, astronomers combine its redshift with a distance indicator independent of that redshift—for example, a relation involving a galaxy’s rotation or a calibrated supernova. Catalogs such as Cosmicflows-4 assemble these measurements to investigate the velocity field and the matter distribution that drives it.[23]
Most such observations constrain radial motion. Reconstructing a three-dimensional flow field adds assumptions and uncertainty, particularly where distances are sparse or noisy. Distance calibration and errors in converting uncertain distances into velocities must also be included when comparing flows with cosmological predictions.[23]
Galaxy evolution has an address
With spectroscopy and complementary observations, researchers compare stellar populations, gas content, and star formation across environments. In the RESOLVE and ECO surveys, many apparent trends near filaments weakened or changed when stellar mass, group membership, and halo mass were considered. Location matters, but a correlation with a filament does not isolate one physical cause.[24]
MaNGA, another SDSS program, adds a different kind of detail: spectra across individual galaxies. It maps internal stellar and gas motions and population differences. This complements large-scale redshift mapping by investigating what happens inside the galaxies that populate the wider web.[25]
Which surveys are extending the map?
DESI: thousands of spectra at once
The Dark Energy Spectroscopic Instrument uses 5,000 robotically positioned fibers on the Mayall telescope. Its main survey began in May 2021. The original observing program was completed in April 2026, and extended observations continue. Observing completion is distinct from completing the cosmological analysis.[26]
DESI’s DR2 cosmological results use three years of observations, including more than 14 million galaxies and quasars. That selected analysis sample should not be confused with the larger total accumulated over the full observing program.[27]
Euclid: imaging and spectroscopy
Euclid is operating, with routine science observations underway since February 2024.[28] Its near-infrared spectroscopy supplies redshifts for galaxy clustering, while imaging supports weak-lensing studies. The imaging and spectroscopic samples differ; imaging billions of galaxies does not mean obtaining billions of precise spectra.[29]
Roman: preparing for science
NASA’s September 2026 update places Roman in commissioning during its journey toward Sun–Earth L2. Instrument checkout and calibration prepare it for its observing program; they are distinct from an already completed cosmological survey.[30]
Another route: the combined glow of hydrogen
21 cm intensity mapping traces neutral hydrogen through aggregate line emission without resolving every galaxy. Different instruments target different redshift ranges; this does not make every hydrogen survey a map of reionization. Foregrounds and instrumental calibration are major challenges.[31]
CHIME’s reported 21 cm auto-power detection demonstrates hydrogen clustering, but its foreground filtering removes the modes needed to recover BAO. A detection of line emission or clustering is therefore a different milestone from a measured acoustic ruler.[32]
Research and mission status checked: 8 September 2026.
Sources and further reading
Original research, scientific reviews, and official survey information. Checked in September 2026. The original illustrations explain structure and measurement methods; they are not observational maps.
- de Lapparent, Geller & Huchra (1986) — A Slice of the UniverseAn influential CfA redshift slice revealed connected concentrations of galaxies surrounding large underdense regions.
- Bolton et al. (2012) — Spectral Classification and Redshift Measurement for BOSSHow spectral templates, fit quality, and repeated observations establish redshifts and their uncertainties.
- Hogg (1999; revised 2000) — Distance measures in cosmologyRedshift, scale factor, and the distinction between comoving, angular-diameter, and luminosity distances.
- Davis & Scrimgeour (2014) — Deriving accurate peculiar velocitiesWhy cosmological and peculiar redshifts combine multiplicatively, and why the simple velocity subtraction can fail.
- Overzier et al. — The Millennium Run Observatory: First LightWhy realistic mock surveys sample galaxies at different cosmic times along the observer’s lightcone.
- Geller & Huchra (1989) — Mapping the UniverseThe expanded CfA survey revealed the Great Wall, a broad sheet of galaxies.
- Colless et al. (2003) — The 2dF Galaxy Redshift Survey: Final Data ReleaseThe final release contains reliable redshifts for 221,414 galaxies, with documented selection and quality information.
- Cole et al. (2005) — The 2dF Galaxy Redshift Survey: Power-Spectrum AnalysisThe final 2dF power spectrum showed the acoustic imprint and constrained cosmology with explicit modeling assumptions.
- Alam et al. (2020/2021) — Two Decades of SDSS, BOSS, and eBOSS CosmologyGalaxies, quasars, and hydrogen absorption extend the acoustic ruler across a wide range of cosmic history.
- Frenk & White (2012) — Dark matter and cosmic structureConnects the cosmic web to gravitational growth and explains why luminous galaxies imperfectly trace matter.
- van de Weygaert & Platen (2009) — Cosmic Voids: Structure, Dynamics and GalaxiesDescribes underdense regions that retain galaxies and substructure, rather than completely empty cosmic cavities.
- Chon, Böhringer & Zaroubi (2015) — On the definition of superclustersExplains why a named supercluster is not automatically one gravitationally bound, relaxed system.
- DESI Collaboration (2024/2025) — Cosmological Constraints from Full-Shape ClusteringClustering beyond the acoustic ruler adds information about structure growth, matter density, and tested departures from general relativity.
- Hamilton (1998) — Linear Redshift Distortions: A ReviewThe distinct effects of coherent infall and random cluster motions on apparent radial structure.
- Ballinger, Peacock & Heavens (1996) — Measuring the cosmological constant with redshift surveysGeometric stretching from an assumed distance relation must be separated from peculiar-velocity distortions.
- DESI Collaboration (2025) — DESI 2024 II: Sample Definitions, Characteristics, and Two-point Clustering StatisticsSurvey selection, random catalogs, instrument corrections, and validation with simulated observations.
- Newman & Gruen (2022) — Photometric Redshifts for Next-Generation SurveysThe precision trade-off of broadband redshifts, and the importance of calibrating full redshift distributions.
- Desjacques, Jeong & Schmidt (2018) — Large-Scale Galaxy BiasWhy galaxies trace matter statistically, with a relationship shaped by galaxy formation and gravitational environment.
- Weinberg et al. (2013) — Observational Probes of Cosmic AccelerationExplains transverse and radial acoustic distances and the combined volume-averaged distance measure.
- Addison et al. (2018) — BAO Measurements and the Hubble Constant DiscrepancyDistinguishes uncalibrated BAO distances from an absolute expansion-rate inference using early-universe information.
- Song & Percival (2009) — Reconstructing the history of structure formation using redshift distortionsWhat the growth combination fσ8 measures and which modelling assumptions enter its interpretation.
- DESI Collaboration (2026) — DR2 Lyman-alpha geometry and dark-energy constraintsAn updated high-redshift geometry measurement complements BAO and modestly shifts combined results toward the standard model.
- Tully et al. (2023) — Cosmicflows-4Combining independent galaxy-distance indicators to estimate radial peculiar motions and their uncertainties.
- Hoosain et al. (2024) — Filaments and galaxy properties in the RESOLVE and ECO surveysSeparates filament proximity from stellar mass, group membership, and halo mass when comparing galaxy properties.
- Bundy et al. (2015) — Overview of the SDSS-IV MaNGA SurveyIntegral-field spectroscopy maps the motions and composition of stars and gas within nearby galaxies.
- Berkeley Lab (15 April 2026) — DESI Completes Its Original Survey and Continues ExploringDESI began its main survey in May 2021, completed the original observations, and continues an extended program.
- DESI Collaboration (2025) — DR2 acoustic-scale measurements and cosmological constraintsThree years of DESI observations deliver precise BAO distances; dark-energy interpretation depends on models and other datasets.
- ESA (24 June 2026) — Euclid’s operating survey and latest data releaseEuclid is an operating survey mission; routine science began in February 2024.
- Euclid Consortium (2023) — Measuring cosmic expansion with BAOEuclid combines near-infrared galaxy spectroscopy for clustering with weak-lensing measurements.
- NASA (updated 7 September 2026) — Roman commissioningRoman is undergoing instrument checkout and calibration while traveling toward Sun–Earth L2.
- Chang and Lidz (2026) — Line-intensity mappingUnresolved line emission could extend acoustic-scale measurements, with foreground removal and calibration as major challenges.
- CHIME Collaboration (2025) — Detection of the 21 cm auto-power spectrumCHIME detects hydrogen clustering, while recovering the BAO scale remains a separate observational challenge.
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 · You are here
- Gravitational Lensing: A Natural Cosmic Telescope
- Measuring the Hubble Constant: The Tension
- Dark Energy Surveys
- Anisotropies and Inhomogeneities
- Current Debates and Outstanding Questions