Charting millions of galaxies to understand large-scale structure, cosmic flows, and expansion
Why Redshift Surveys Matter
For centuries, astronomy primarily cataloged objects as points on a two-dimensional sky. The third dimension, distance, remained elusive until the modern era. As Hubble’s law showed that a galaxy’s recession velocity (v) is approximately proportional to its distance (d) (especially at low redshifts), measuring a galaxy’s redshift (the shift in its spectral lines) became a practical way to gauge cosmic distances. By systematically gathering redshifts for large samples of galaxies, we obtain three-dimensional maps of the universe’s structure—filaments, clusters, voids, and superclusters.
These large-scale surveys form a cornerstone of observational cosmology today. They reveal the cosmic web, shaped by dark matter and primordial density fluctuations, and they help measure cosmic flows, expansion history, and the geometry and composition of the universe. Below, we survey how redshift surveys work, what they’ve discovered, and the role they play in determining key cosmological parameters (dark energy, dark matter content, Hubble constant, etc.).
2. Basics of Redshift and Cosmological Distance
2.1 Redshift Definition
A galaxy’s redshift (z) is defined by:
z = (λobserved - λemitted) / λemitted,
indicating how much its spectral features are shifted to longer wavelengths. For nearby galaxies, z ≈ v/c, linking velocity (v) and speed of light (c). Farther out, cosmic expansion complicates the direct velocity interpretation, but we still rely on z as a measure of how much the universe has stretched since the photon was emitted.
2.2 Hubble’s Law and Beyond
At low redshift (z ≪ 1), Hubble’s law states v ≈ H0 d. Thus, a redshift-based velocity can yield a distance approximation d ≈ (c/H0) z. At higher redshifts, one adopts a full cosmological model (ΛCDM, for instance) to relate z to comoving distance. Redshift surveys thus rest on measuring spectra, identifying known lines (e.g., hydrogen Balmer lines, [O II], etc.), and converting redshift to distance to build 3D maps of galaxies.
3. Historical Evolution of Redshift Surveys
3.1 CfA Redshift Survey
One of the earliest large redshift surveys was the Center for Astrophysics (CfA) Survey (1970s–1980s), amassing thousands of galaxy redshifts. The resulting 2D “wedge” plots showed walls and voids, including the “Great Wall.” These features indicated that galaxy distribution was far from uniform, unveiling large-scale structure at scales of ~100 Mpc.
3.2 Two-Degree Field (2dF) and Early 2000s
In the early 2000s, the 2dF Galaxy Redshift Survey (2dFGRS) used the 2dF multi-fiber spectrograph on the Anglo-Australian Telescope, measuring ~220,000 redshifts out to z ∼ 0.3. This survey provided robust detections of baryon acoustic oscillations (BAO) in the galaxy correlation function, refining matter density estimates. It also mapped large voids, filaments, and large-scale flows in unprecedented detail.
3.3 SDSS: A Revolutionary Catalog
Launched in 2000, the Sloan Digital Sky Survey (SDSS) used a dedicated 2.5 m telescope with wide-field CCD imaging plus multi-fiber spectroscopy. Over multiple phases (SDSS-I, II, III, IV), it collected millions of galaxy spectra, covering substantial fractions of the northern sky. Sub-projects included:
- BOSS (Baryon Oscillation Spectroscopic Survey): ~1.5 million luminous red galaxies, pushing BAO detections to high precision.
- eBOSS: Extended BAO to higher redshift using emission-line galaxies, quasars, and Lyα forest.
- MaNGA: Detailed integral-field spectroscopy of thousands of galaxies.
SDSS’s impact was enormous: unveiling the cosmic web in 3D, refining the power spectrum of galaxy clustering, and confirming ΛCDM parameters with strong evidence for dark energy [1,2].
3.4 DESI, Euclid, Roman, and Future
DESI (Dark Energy Spectroscopic Instrument) began in 2020, targeting ~35 million galaxy/quasar redshifts, ~z up to 3.5, revolutionizing cosmic cartography. Future missions:
- Euclid (ESA) aims for wide-field imaging and spectroscopy out to z ∼ 2.
- Nancy Grace Roman Space Telescope (NASA) will similarly map large areas in near-IR, measuring BAO and weak lensing.
Together with intensity mapping arrays (SKA for 21 cm lines), these programs will push large-scale structure measurements to new redshift regimes, further constraining dark energy and the expansion history.
4. Large-Scale Structure: The Cosmic Web
4.1 Filaments and Nodes
Redshift surveys show filaments: elongated structures, tens to hundreds of Mpc long, connecting dense “nodes” or clusters. At the intersections of filaments lie clusters—the densest galaxy environments—while superclusters form bigger, loosely bound structures. Galaxies in filaments can follow characteristic flows, feeding material into cluster nodes.
4.2 Voids
Between filaments lie voids: large underdense regions lacking bright galaxies. Voids can measure ~10–50 Mpc across or more, occupying most cosmic volume but hosting few galaxies. Mapping voids helps test dark energy, as expansion in these emptier regions can be slightly faster, providing complementary constraints on cosmic flow and gravity.
4.3 The Tapestry
Combined, filaments, clusters, superclusters, and voids form a web— a “foam-like” structure predicted by N-body simulations of dark matter. Observations confirm that dark matter provides the underlying gravitational scaffolding, while baryonic matter (stars, gas) traces that structure. Redshift surveys made this cosmic web visually and quantitatively evident.
5. Cosmology from Redshift Surveys
5.1 Correlation Functions and Power Spectra
A key tool is the two-point correlation function ξ(r), describing the excess probability of finding a galaxy pair separated by distance r over random. We also examine the power spectrum P(k) in Fourier space. The shape of P(k) reveals matter density, baryon fraction, neutrino mass scale, and initial fluctuation spectrum. Combining with CMB data yields precise fits to ΛCDM.
5.2 Baryon Acoustic Oscillations (BAO)
One of the prime features in galaxy clustering is the BAO signal—a weak peak at ~100–150 Mpc scale in the correlation function. Since that scale is well-known from early-universe physics, it acts as a “standard ruler” to measure cosmic distances vs. redshift. By comparing the measured BAO scale with the predicted physical size, we derive the Hubble parameter H(z). This helps constrain dark energy’s equation of state, geometry, and cosmic expansion history.
5.3 Redshift-Space Distortions (RSD)
Galaxies’ peculiar velocities along the line of sight cause “redshift-space distortions,” creating anisotropy in the correlation function. RSD encodes the growth rate of cosmic structure, thus testing whether gravity is standard (GR) or modified. Observed RSD data so far align well with GR predictions, but ongoing/future surveys improve precision, possibly detecting small deviations if new physics emerges.
6. Mapping Cosmic Flows
6.1 Peculiar Velocities and Local Group Motion
In addition to Hubble flow, galaxies have peculiar velocities from local mass concentrations, e.g., the Virgo Cluster, the Great Attractor. Surveys that combine redshifts and independent distance indicators (Tully–Fisher, supernovae, surface brightness fluctuations) can measure these velocity fields. The resulting “cosmic flow maps” show bulk flows of hundreds of km/s over ~100 Mpc scales.
6.2 Bulk Flow Debates
Some analyses claim large-scale flows exceeding ΛCDM expectations, though systematic uncertainties remain. Clarifying these cosmic flows provides another handle on dark matter distribution and possible new gravitational effects. The synergy of redshift surveys with robust distance measurements continues to refine cosmic velocity maps.
7. Overcoming Challenges and Systematics
7.1 Selection Function and Completeness
Galaxies in a redshift survey are typically magnitude-limited or selected by color. Variations in selection or target completeness can bias the measured clustering. Survey teams carefully model completeness across sky patches and correct for radial selection (fewer faint galaxies at larger distance). This ensures the final correlation function or power spectrum is not artificially distorted.
7.2 Redshift Errors and Photometric Approaches
Spectroscopic redshifts can be accurate to Δz ≈ 10-4. But large photometric surveys (like the Dark Energy Survey, LSST) rely on broad-band filters, giving Δz ≈ 0.01–0.1. While photometric redshifts enable huge sample sizes, they have increased uncertainty in the line-of-sight direction. Methods like clustering-based redshift calibration or cross-correlation with spectroscopic samples help mitigate these uncertainties.
7.3 Nonlinear Evolution and Galaxy Bias
On small scales, galaxy clustering becomes strongly nonlinear, with “finger-of-god” effects in redshift space and complexities from mergers. Also, galaxies do not perfectly trace dark matter; there’s a “galaxy bias” factor that depends on environment and type. Careful modeling or focusing on large scales (where linear approximations hold) is often used to reliably extract cosmological information.
8. Latest and Future Redshift Surveys
8.1 DESI
The Dark Energy Spectroscopic Instrument (DESI) on the Mayall 4 m telescope (Kitt Peak) started surveying in 2020, aiming for 35 million spectra of galaxies and quasars. With 5000 robotic positioners for optical fibers, it can measure thousands of redshifts per exposure, spanning z ∼ 0.05–3.5. DESI’s unprecedented sample will refine BAO distance measurements at multiple epochs, pin down cosmic expansion and the growth of structure, and yield invaluable data for galaxy evolution studies.
8.2 Euclid and Nancy Grace Roman Space Telescope
Euclid (ESA) and the Roman Space Telescope (NASA) in the late 2020s will combine near-IR imaging and spectroscopy to map billions of galaxies out to z ∼ 2. They will measure both weak lensing and BAO, providing robust constraints on dark energy, potential cosmic curvature, and neutrino mass. Meanwhile, synergy with ground-based spectrographs and future intensity mapping arrays (e.g., SKA for 21 cm lines) will further expand the cosmic volume surveyed.
8.3 21 cm Intensity Mapping
An emerging technique is 21 cm intensity mapping, measuring large-scale HI emission without resolving individual galaxies. Arrays like CHIME, HIRAX, and SKA can map BAO signals in neutral hydrogen to higher redshifts, bridging reionization epochs. This approach offers another route to cosmic expansion constraints beyond optical/IR redshift surveys, though calibration challenges remain.
9. Broader Impact: Dark Energy, Hubble Tension, and More
9.1 Dark Energy Equation of State
Combining BAO distance scales at various redshifts with the CMB’s anchor at z = 1100 and supernova data at low z provides the expansion history H(z). This determines if dark energy is truly a cosmological constant (w = -1) or if it varies over time. Thus far, no strong evidence for w ≠ -1 has been found, but improved BAO data might reveal subtle deviations.
9.2 Hubble Tension
Some local distance-ladder measurements of H0 exceed the ~67–68 km/s/Mpc from Planck + BAO fits by 4–5σ. This “Hubble tension” may highlight either systematic errors or new physics (e.g., early dark energy). More precise BAO from DESI, Euclid, etc. will further clarify the cosmic expansion at intermediate redshifts, potentially bridging or intensifying the tension.
9.3 Galaxy Evolution
Redshift surveys also enable galaxy evolution studies: the star formation history, morphological transformations, environment dependencies. By comparing galaxy properties across cosmic time, we glean how quenching, mergers, and gas inflows shape the population distribution. The cosmic web context (filaments vs. voids) influences these processes, linking small-scale galaxy evolution to large-scale structure.
10. Conclusion
Redshift surveys are an essential tool of observational cosmology, providing three-dimensional maps of millions of galaxies. This 3D perspective reveals the cosmic web—filaments, clusters, and voids—and delivers robust measurements of large-scale structure. Key breakthroughs include:
- Baryon Acoustic Oscillations (BAO): A standard ruler for cosmic distances, constraining dark energy.
- Redshift-Space Distortions: Gauging structure growth and gravity.
- Galaxy Flows and environment: Tracing cosmic velocity fields, environment-driven evolution.
Major surveys from CfA to 2dF, SDSS, and BOSS/eBOSS validated ΛCDM by capturing the cosmic web in detail. Next-generation efforts—DESI, Euclid, Roman, 21 cm mapping—promise to expand redshift coverage, sharpen BAO distance measures, and possibly resolve tensions in the Hubble constant or detect new physics. Thus, redshift surveys remain at the forefront of precision cosmology, illuminating how the universe’s large-scale structure grows and how cosmic expansion is driven by dark matter and dark energy.
References and Further Reading
- de Lapparent, V., Geller, M. J., & Huchra, J. P. (1986). “A slice of the universe.” The Astrophysical Journal Letters, 302, L1–L5.
- Eisenstein, D. J., et al. (2005). “Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies.” The Astrophysical Journal, 633, 560–574.
- Cole, S., et al. (2005). “The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final data set and cosmological implications.” Monthly Notices of the Royal Astronomical Society, 362, 505–534.
- Alam, S., et al. (2021). “Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys.” Physical Review D, 103, 083533.
- DESI Collaboration: desi.lbl.gov (accessed 2023).