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Redshift is the phenomenon wherein the wavelength of electromagnetic radiation emitted by an astronomical object is observed to increase, shifting the light toward the longer-wavelength (redder) end of the spectrum when received by an observer. This effect is quantified by the redshift parameter

z = \frac{\lambda_\mathrm{observed} - \lambda_\mathrm{rest}}{\lambda_\mathrm{rest}}

. It arises from three primary mechanisms: Doppler redshift, caused by the relative motion of the source away from the observer; gravitational redshift, resulting from the influence of a strong gravitational field on light; and cosmological redshift, due to the expansion of spacetime itself stretching the light's wavelength as it travels across the universe.^[1]^[2] The Doppler redshift, the most familiar type, follows from the classical Doppler effect extended to relativistic speeds, where the recession of the emitting object elongates the wavefronts of light, increasing their wavelength proportionally to the velocity of separation. In astrophysics, this is commonly observed in binary star systems, galactic rotation curves, and the peculiar velocities of nearby galaxies, allowing astronomers to infer motions on scales up to thousands of kilometers per second. Unlike the other types, Doppler redshift can produce a blueshift (wavelength decrease) if the object approaches the observer, as seen in some local galaxies like Andromeda.^[3]^[4] Gravitational redshift, a prediction of Albert Einstein's general theory of relativity published in 1915, occurs when light escapes from a region of intense gravity, such as near a neutron star or black hole, losing energy and thus lengthening its wavelength due to the warping of spacetime. This effect was first experimentally verified in the Pound-Rebka experiment conducted at Harvard University in 1959–1960, where researchers measured a fractional wavelength shift of approximately 2.5 × 10^{-15} in gamma rays transmitted upward through a 22.5-meter tower against Earth's gravitational field, confirming the prediction to within 10% accuracy. In stellar contexts, gravitational redshift provides insights into the mass-radius relations of compact objects like white dwarfs and pulsars.^[5]^[6] Cosmological redshift dominates observations of distant galaxies and quasars, reflecting the uniform expansion of the universe rather than peculiar motions or local gravity. In 1929, Edwin Hubble analyzed spectra from the Mount Wilson Observatory and established that the redshift

z

of galaxies is directly proportional to their distance

d

, formalized as Hubble's law:

v = H_0 d

, where

v = c z

is the recession velocity (for small

z

) and

H_0

is the Hubble constant, estimated at approximately 70 km/s/Mpc (as of 2025, though values range from 67–74 km/s/Mpc due to measurement tensions).^[7] This discovery provided key evidence for the Big Bang model, enabling distance measurements to objects billions of light-years away and revealing the universe's accelerating expansion driven by dark energy. Redshift surveys, such as those from the Sloan Digital Sky Survey, continue to map cosmic structure and evolution.^[8]^[9]

Definition and Fundamentals

Conceptual Overview

Redshift refers to the increase in the observed wavelength of electromagnetic radiation emitted by a source, causing spectral features to shift toward longer wavelengths, which correspond to the red end of the visible spectrum. This phenomenon is quantified by the dimensionless parameter

z = \frac{\lambda_\text{observed} - \lambda_\text{emitted}}{\lambda_\text{emitted}}

, where

\lambda_\text{observed}

is the measured wavelength and

\lambda_\text{emitted}

is the wavelength at emission; values of

z > 0

indicate a wavelength elongation, typically signifying recession of the source relative to the observer.^[10] Intuitively, redshift can be visualized as the stretching of light waves, akin to marks on a rubber band being pulled apart: as space expands between the emitter and observer, the wavelengths lengthen proportionally, transforming shorter (bluer) light into longer (redder) light. For example, prominent spectral lines like those in the hydrogen Balmer series—such as the Hα line at 656 nm (red) or Hβ at 486 nm (blue-green) in the rest frame—appear displaced to even longer wavelengths in distant objects, moving progressively toward the infrared as

z

increases.^[11]^[12] Although redshift often manifests as an apparent reddening of an object's overall color, it is distinctly a precise relocation of discrete spectral lines, detectable and quantifiable only through detailed spectroscopic analysis rather than simple visual or photometric observation. The first recorded detection of redshift occurred in 1912 when Vesto Slipher measured the spectrum of the Sombrero Galaxy (NGC 4594), revealing a substantial line shift equivalent to a recession velocity of approximately 1100 km/s. This shift arises from mechanisms such as the Doppler effect due to relative motion or cosmological expansion, though the underlying causes are explored in greater detail elsewhere.

Measurement and Quantification

Spectroscopic methods provide the most precise measurements of redshift by directly resolving spectral lines shifted from their rest-frame wavelengths. These techniques typically employ diffraction gratings or Fabry-Pérot interferometers to disperse and analyze light from astronomical sources. Diffraction gratings, often volume-phase holographic (VPH) types, are optimized for high spectral resolution (R = λ/Δλ typically 3000–5000) and throughput up to 90%, enabling the separation of closely spaced emission or absorption lines essential for accurate redshift determination. For instance, VPH gratings in integral-field spectrographs couple spatial and spectral information via fibers, lenslets, or slicers, facilitating redshift surveys of galaxies by measuring line shifts with minimal loss in signal-to-noise ratio (S/N). Fabry-Pérot interferometers, alternatively, achieve ultra-high resolution (R up to 10^5) through interference patterns formed by multiple etalons, ideal for detecting narrow lines in high-redshift objects or resolving velocity dispersions that contribute to redshift precision. These instruments excel in low-to-moderate redshift regimes but require high S/N to avoid blending of lines. Photometric redshift estimation offers a complementary approach for faint or numerous objects where spectroscopy is impractical, relying on broadband photometry rather than resolved spectra. This method involves template fitting, where observed colors in multiple filters are matched to synthetic spectral energy distribution (SED) templates of galaxies or quasars, inferring redshift from the best-fit shift.^[13] Template fitting is physically motivated and can provide full probability distributions but is sensitive to incomplete template libraries and degeneracies between redshift and intrinsic properties like dust extinction.^[13] Machine learning techniques, such as neural networks or random forests trained on spectroscopic samples, have emerged as powerful alternatives, achieving higher accuracy within the training redshift range by learning complex color-redshift relations from large datasets in surveys like LSST or DESI.^[13] Hybrid approaches combining both methods reduce errors by over 10% in some cases, particularly for extragalactic populations.^[13] Redshift measurements are subject to several error sources that can bias results or increase uncertainties. Instrumental resolution limits the ability to resolve fine spectral features, with low-resolution spectrographs (R < 1000) leading to line blending and redshift uncertainties up to Δz ~ 0.001. Signal-to-noise ratio (S/N) is a primary factor, as low S/N in faint objects amplifies noise in line centroiding, contributing Gaussian-distributed errors of Δz ~ 10^{-4} from thermal motions or turbulence. In photometric methods, template mismatches—arising from unrepresentative SED models—introduce systematic biases, particularly at high redshifts where unobserved emission lines skew fits, resulting in catastrophic outliers up to 5% of cases. These errors are mitigated through cross-correlation with empirical templates and Monte Carlo simulations to quantify velocity dispersions (e.g., 85–300 km/s for luminous red galaxies). Redshift z is a dimensionless quantity defined as z = (λ_observed - λ_rest)/λ_rest, with spectroscopic methods achieving typical precisions of Δz ≈ 0.001 for bright sources, sufficient to resolve velocity differences of ~200 km/s.^[14] Photometric estimates are coarser, with standard deviations σ_z ≈ 0.05 (or normalized median absolute deviation σ_NMAD ~ 0.02–0.03), enabling statistical studies but not individual velocity measurements. For example, nearby galaxies at z ≈ 0.1, such as those in the Virgo Cluster, yield spectroscopic redshifts precise to 0.0005, while photometric values for similar objects scatter by ~0.01 due to color uncertainties. Key telescopes and their spectrographs play crucial roles in redshift quantification across cosmic scales. The Hubble Space Telescope's Space Telescope Imaging Spectrograph (STIS) provides ultraviolet-to-optical spectra for resolving lines in nearby and intermediate-redshift galaxies, achieving resolutions up to R = 30,000 for precise z measurements.^[15] At the Very Large Telescope (VLT), instruments like FORS2 and VIMOS deliver multi-object spectroscopy with Δz ~ 0.001 for surveys of thousands of objects, while the integral-field unit MUSE offers spatially resolved redshifts at R = 3000 for galaxy kinematics.^[14]^[16] The James Webb Space Telescope's Near-Infrared Spectrograph (NIRSpec) extends capabilities to high redshifts (z > 10) in the 0.6–5.3 μm range, using microshutters for simultaneous spectroscopy of up to 100 faint sources, enabling high redshift success rates, such as approximately 74% in recent deep-field surveys of early universe galaxies.^[17]^[18]

Historical Development

Early Observations

Vesto Slipher, working at the Lowell Observatory, pioneered the measurement of radial velocities for spiral nebulae using high-resolution spectroscopy starting in 1912. His initial observation of the Andromeda Nebula (M31, NGC 224) revealed a blueshift of approximately −300 km/s, indicating it was approaching the Milky Way. Subsequent observations of other spirals showed predominantly large redshifts. By 1917, Slipher had measured velocities for 25 spiral nebulae, with values ranging from −300 km/s to +1100 km/s and a mean recession velocity of about +400 km/s; 21 were receding while 4 were approaching. These unexpectedly high velocities—far exceeding typical stellar motions of around 20 km/s—were initially interpreted as peculiar motions, but they provided crucial data that later supported the concept of cosmic expansion.^[19]^[20]

Theoretical Milestones

In 1922, Alexander Friedmann derived solutions to Einstein's field equations of general relativity that permitted a dynamic, expanding universe, challenging the prevailing static model and laying the foundation for the Friedmann-Lemaître-Robertson-Walker (FLRW) metric.^[21] These solutions described a homogeneous and isotropic universe with a scale factor that evolves over time, incorporating positive, zero, or negative spatial curvature depending on the density parameter.^[22] Friedmann's work was initially overlooked but later recognized as seminal when Howard Robertson and Arthur Walker independently developed similar frameworks in the early 1930s, formalizing the FLRW models that became central to relativistic cosmology.^[23] Building on Friedmann's ideas, Georges Lemaître proposed in 1927 an expanding universe model that interpreted the observed redshifts of distant galaxies as evidence of cosmic expansion rather than peculiar velocities alone.^[24] Lemaître's "primeval atom" hypothesis, elaborated in subsequent works, posited that the universe originated from a hot, dense state and expanded, with redshifts arising from the cumulative Doppler-like effect of this recession. This framework integrated general relativity with emerging astronomical data, estimating a Hubble-like constant and predicting that redshift-distance relations would reveal the universe's finite age.^[25] During the 1930s and 1940s, Richard Tolman and Hermann Bondi developed theoretical tests to distinguish between kinematic interpretations of expansion (pure velocity recession) and dynamic ones governed by general relativity. Tolman's surface brightness test predicted that in an expanding universe, the observed surface brightness of galaxies should dim with redshift as (1 + z)^{-4} due to cosmological effects on flux and angular size. Bondi extended this with spherically symmetric dust models in 1947, analyzing how inhomogeneities could mimic or challenge uniform expansion, providing tools to probe whether redshifts reflected true relativistic dynamics. The steady-state theory, introduced by Hermann Bondi, Thomas Gold, and Fred Hoyle in 1948, offered an alternative explanation for redshifts without invoking a Big Bang origin.^[26] This model assumed continuous matter creation to maintain constant density amid expansion, satisfying the perfect cosmological principle and attributing redshifts solely to recession in an eternal, unchanging universe. Though mathematically consistent with general relativity, it was later falsified by the 1965 discovery of the cosmic microwave background, which supported a hot early universe over steady-state predictions.^[27] The discovery of quasars in the 1960s, particularly Maarten Schmidt's 1963 identification of 3C 273's redshift of z = 0.158, revealed objects with enormous luminosities at high redshifts, necessitating refinements to relativistic cosmology.^[28] These findings implied quasars as active galactic nuclei powered by supermassive black holes, with high-z examples (up to z ≈ 2 by mid-decade) probing the early universe and confirming FLRW predictions of accelerated expansion rates at greater distances.^[29] This spurred developments in understanding redshift evolution and the role of dark matter in structure formation within expanding models.^[30]

Physical Mechanisms

Doppler Redshift

The Doppler redshift arises from the relative motion between a light source and an observer, where the source recedes along the line of sight, causing the observed wavelength of emitted light to increase compared to its rest-frame value.^[31] This effect is a direct consequence of the Doppler principle applied to electromagnetic waves, distinct from expansions of space or gravitational fields. In astronomical contexts, it manifests as a shift in spectral lines toward longer wavelengths, enabling measurements of radial velocities.^[32] For non-relativistic speeds where the radial velocity

v

is much less than the speed of light

c

(i.e.,

v \ll c

), the redshift parameter

z

, defined as

z = \frac{\lambda_\text{obs} - \lambda_\text{rest}}{\lambda_\text{rest}}

, approximates

z \approx \frac{v}{c}

.^[33] This classical formula derives from the wave nature of light, where the receding source stretches the wavefronts, increasing the observed wavelength proportionally to the velocity component away from the observer. In special relativity, the full Doppler redshift accounts for the constancy of light speed and Lorentz invariance, derived by applying the Lorentz transformation to the events of photon emission and reception. Consider a source emitting light at proper frequency

f_\text{rest}

(wavelength

\lambda_\text{rest} = c / f_\text{rest}

) while moving radially away from a stationary observer at velocity

v

, with

\beta = v/c

. The Lorentz transformation for the time interval between two wavefront emissions in the observer's frame yields the observed frequency

f_\text{obs} = f_\text{rest} \sqrt{\frac{1 - \beta}{1 + \beta}}

fobs=frest1+β1−β

, leading to the redshift formula: $z = \sqrt{\frac{1 + \beta}{1 - \beta}} - 1.$

−1. This longitudinal case applies to direct line-of-sight recession. For transverse motion, where the source velocity is perpendicular to the line of sight at the moment of emission, the effect stems purely from time dilation, giving $z = \gamma - 1$ , where $\gamma = 1 / \sqrt{1 - \beta^2}$

.^[34]^[35] These formulas find key applications in measuring motions within stellar and galactic systems. In binary star systems, periodic Doppler shifts in spectral lines reveal orbital velocities, allowing determination of stellar masses and inclinations.^[36] For exoplanet detection via the radial velocity method, the star's wobble induced by an orbiting planet produces subtle redshifts and blueshifts, with amplitudes as small as meters per second.^[32] Galactic rotation curves, such as that of the Milky Way, use Doppler shifts from neutral hydrogen emission lines to map velocities, typically around 220 km/s at the solar radius, indicating flat rotation profiles out to several kiloparsecs.^[37] Doppler redshift primarily probes local peculiar velocities—random motions superimposed on larger-scale flows—typically below 1,000 km/s for galaxies in clusters, in contrast to the systematic Hubble flow dominating at greater distances.^[38] This distinction aids in separating motion-induced effects from cosmological expansion in nearby universe studies.^[39]

Cosmological Redshift

Cosmological redshift arises from the expansion of the universe, as described by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, which models a homogeneous and isotropic expanding spacetime. The FLRW metric is given by

ds^2 = -c^2 dt^2 + a(t)^2 \left[ \frac{dr^2}{1 - k r^2} + r^2 d\Omega^2 \right],

where

a(t)

is the scale factor that describes the relative expansion of space as a function of cosmic time

t

r

is the comoving radial coordinate,

k

is the curvature parameter (

k = 0

for a flat universe,

k > 0

for closed, and

k < 0

for open), and

d\Omega^2 = d\theta^2 + \sin^2\theta d\phi^2

accounts for angular coordinates.^[40] For light propagating along null geodesics (

ds = 0

), the radial path satisfies

c \, dt = a(t) \, dr / \sqrt{1 - k r^2}

cdt=a(t)dr/1−kr2

. The redshift $z$ for a photon emitted at cosmic time $t_e$ and observed at $t_0$ (present time) emerges from the stretching of the photon's wavelength proportional to the scale factor: $1 + z = a(t_0) / a(t_e)$ . This relation indicates that the observed wavelength is stretched by the factor by which the universe has expanded between emission and observation.^[41] This redshift represents a cumulative effect integrated over the photon's path through the evolving expansion history of the universe, rather than a local velocity shift. Light emitted at an earlier epoch, when the scale factor was smaller, experiences progressive stretching as space expands during transit, leading to a longer observed wavelength compared to the emitted one. Unlike the Doppler redshift, which stems from relative motion through space, cosmological redshift involves no bulk peculiar motion of the source; instead, it is a global metric effect where comoving observers and sources remain at fixed coordinates while distances between them increase. This distinction is tested observationally: if cosmological redshift were purely Doppler-like, distant galaxies would exhibit enormous transverse proper motions (superluminal in many cases) to account for the radial velocity interpretation, but astrometric measurements reveal only modest proper motions consistent with local dynamics, not recession speeds. Additionally, supernova light curves at high redshift are observed to be dilated in time by a factor of $1 + z$ , matching the expected expansion effect rather than a static Doppler broadening.^[42] At low redshifts ( $z \ll 1$ ), cosmological redshift integrates with Hubble's law, where the recession speed $v \approx c z$ relates linearly to distance $d$ as $c z = H_0 d$ , with $H_0$ the present-day Hubble constant. This empirical relation, first established from observations of extra-galactic nebulae, provides a direct measure of cosmic expansion for nearby objects. For higher redshifts, deviations from linearity arise due to the universe's deceleration or acceleration history, incorporating the deceleration parameter $q_0$ (measuring slowdown from gravity) and the cosmological constant $\Lambda$ (driving late-time acceleration). The redshift-distance relation expands as a series: $c z \approx H_0 d \left[1 + \frac{1 - q_0}{2} z + \cdots \right]$ , with further terms involving $\Lambda$ and higher-order parameters, enabling distance estimates that probe the universe's composition and evolution. In the local universe, small Doppler contributions from peculiar velocities can slightly contaminate this relation, but they become negligible at larger distances where cosmological effects dominate.^[43]^[40]

Gravitational Redshift

Gravitational redshift arises in general relativity as a consequence of the warping of spacetime by mass, causing light emitted from a region of deeper gravitational potential to appear shifted toward longer wavelengths when observed from a region of shallower potential. This effect stems from the time dilation experienced by clocks in stronger gravitational fields, as photons climbing out of a potential well lose energy, reducing their frequency. In the weak-field limit, the redshift parameter

z

is given by

z \approx \Delta \Phi / c^2

, where

\Delta \Phi

is the difference in gravitational potential between emission and observation points, and

c

is the speed of light. This formula can be derived from the equivalence principle, equating a uniform gravitational field to an accelerating frame, where the frequency shift matches the Doppler effect from relative motion.^[44] The Pound-Rebka experiment in 1959 provided the first laboratory confirmation of this effect, measuring the redshift of gamma rays traveling upward 22.5 meters against Earth's gravity using the Mössbauer effect at Harvard's Jefferson Laboratory. By comparing absorption resonances between source and detector, they detected a fractional frequency shift of

(2.57 \pm 0.18) \times 10^{-15}

, aligning with the predicted

z = g h / c^2

(where

g

is gravitational acceleration and

h

is height) to within 10% accuracy, later refined to 1%. This verified the equivalence principle's prediction for gravitational redshift in a terrestrial setting. In the Schwarzschild metric, describing spacetime around a spherically symmetric, non-rotating mass

M

, the full relativistic treatment emerges from solving the null geodesic equations for photons. The metric is

ds^2 = -(1 - 2GM/(c^2 r)) c^2 dt^2 + (1 - 2GM/(c^2 r))^{-1} dr^2 + r^2 d\Omega^2

, where

G

is the gravitational constant. For radial light rays, the conserved energy-like quantity from the geodesic equation yields the frequency shift:

1 + z = 1 / \sqrt{1 - 2GM/(c^2 r)}

1+z=1/1−2GM/(c2r)

, with $r$ the radial coordinate of emission. In the weak-field approximation ( $2GM/(c^2 r) \ll 1$ ), this reduces to $z \approx GM/(c^2 r)$ , matching the Newtonian potential form. This derivation highlights how curvature alters photon paths and energies along geodesics. Astrophysical tests include solar observations, where Einstein predicted a redshift corresponding to $z \approx 2.12 \times 10^{-6}$ from the Sun's surface potential. This has been verified through high-precision spectroscopy of solar spectral lines, such as iron transitions, with a 2020 analysis of HARPS data yielding z ≈ (2.13 ± 0.02) × 10^{-6}, consistent with general relativity after accounting for Doppler broadening and solar rotation. Such measurements, often using eclipse data to isolate limb effects, confirm the prediction originally tied to 1919 eclipse expeditions testing broader relativistic effects.^[45] In compact objects, the effect scales dramatically with mass-to-radius ratio. For white dwarf atmospheres, like Sirius B (mass $\approx 1 M_\odot$ , radius $\approx 0.0084 R_\odot$ ), spectra show $z \sim 10^{-4}$ (e.g., 80.65 km/s equivalent shift), measured via Hubble Space Telescope observations of Balmer lines, enabling mass-radius constraints. Neutron stars exhibit stronger shifts, up to $z \approx 0.3$ for typical 1.4 $M_\odot$ objects with 10-15 km radii, inferred from X-ray burst spectroscopy and pulsar timing, where line broadening encodes the potential depth. At a black hole's event horizon ( $r = 2GM/c^2$ ), the redshift diverges to infinity, as the metric factor vanishes, rendering emitted light unobservable from afar due to infinite energy loss along outgoing geodesics.^[46]^[47]

Astronomical Observations

Local Universe Studies

Studies of the local universe, typically encompassing objects at redshifts z < 0.1, leverage redshift measurements to map peculiar velocities—deviations from the uniform Hubble expansion—revealing the gravitational dynamics shaping nearby structures. Redshift distortions arise primarily from the Doppler effect due to these peculiar motions, which elongate galaxy clustering patterns along the line of sight, as predicted by linear theory in the Kaiser effect. This effect, where coherent infall toward overdensities boosts the apparent power on large scales in redshift space, enables reconstruction of velocity fields from galaxy surveys. For instance, maps of peculiar velocities around the Virgo Cluster (at approximately 16 Mpc) show infall velocities of about 200-300 km/s, highlighting its role as a dominant gravitational attractor in the local volume.^[48]^[49] The Tully-Fisher relation provides a key tool for calibrating distances to spiral galaxies in this regime, correlating infrared luminosity (from 2MASS photometry) with neutral hydrogen line widths as a proxy for rotational velocity, enabling redshift-independent distance estimates accurate to within 20% out to 100 Mpc. By comparing these distances to observed redshifts, peculiar velocities are derived as v_pec = cz - H_0 d, isolating local motions from the Hubble flow. This method has been instrumental in mapping velocity fields for thousands of galaxies, confirming anisotropic structures like the "Great Attractor" influencing motions over scales of 50-100 Mpc.^[50] Within the Local Group, redshift studies highlight contrasting dynamics: while most members recede due to the cosmological expansion, the Andromeda Galaxy (M31) exhibits a blueshift of z ≈ -0.001, corresponding to a radial approach velocity of about -300 km/s relative to the Milky Way, driven by mutual gravitational attraction. This peculiar motion exemplifies how local group-scale interactions override the general recession in the nearby universe (z < 0.01). Surveys like the 6dF Galaxy Survey (6dFGS), covering over 88,000 galaxies to z ≈ 0.05, and the 2MASS Redshift Survey (2MRS) extended to the Two-Micron All-Sky Redshift Survey (2MASS), have detected velocity anomalies such as bulk flows exceeding 400 km/s toward the Shapley Supercluster, using fundamental plane distances for early-type galaxies in 6dFGS and Tully-Fisher for spirals in 2MASS.^[51] To isolate peculiar velocities, observed redshifts are corrected by subtracting the expected Hubble flow contribution, cz_H = H_0 d, where d is obtained from independent indicators like Cepheid variables or surface brightness fluctuations for calibration. This correction is crucial at low z, where peculiar velocities can contribute up to 10-20% of the total redshift signal, and is applied iteratively in velocity field reconstructions to account for non-linear effects near clusters. Such analyses from local surveys confirm a growth rate of structure fσ_8 ≈ 0.4-0.5 at z ≈ 0, consistent with ΛCDM predictions.^[52]^[53]

Extragalactic Detections

Extragalactic redshift detections have provided crucial insights into the large-scale structure and evolution of the universe beyond the Local Group, revealing patterns of galaxy assembly and intergalactic medium (IGM) properties at moderate redshifts. Observations of quasars, which exhibit prominent broad emission lines in their spectra due to high-velocity gas in accretion disks around supermassive black holes, span a wide redshift range from approximately z=0.1 to z=7, allowing probes of cosmic history over billions of years. A seminal example is the quasar 3C 273, the first identified with a spectroscopic redshift of z=0.158, discovered through analysis of its optical spectrum showing redshifted hydrogen emission lines.^[28] These broad lines, typically with full widths at half maximum exceeding 1000 km/s, enable precise redshift measurements and highlight the role of quasars as beacons for tracing the growth of cosmic structures. Galaxy clusters, as cataloged in the Abell survey, offer another key avenue for extragalactic redshift studies, with the original compilation identifying 4073 rich clusters at redshifts up to z=0.2 and a typical mean redshift around z≈0.18.^[54] Redshift surveys of these clusters reveal infall patterns, where galaxies approach cluster centers at velocities up to several hundred km/s, indicative of gravitational collapse and the formation of massive structures in the cosmic web. Such observations link redshift data to the dynamics of cluster environments, providing evidence for the hierarchical buildup of dark matter halos at these distances. The Lyman-alpha forest, consisting of numerous narrow absorption lines in quasar spectra from neutral hydrogen in the diffuse IGM, traces the filamentary structure of the universe at intermediate redshifts of z=1–3. These redshifted absorption features, appearing as a "forest" blueward of the quasar's Lyman-alpha emission line, reveal density fluctuations in the IGM that correlate with the underlying dark matter distribution, offering a window into the epoch of structure formation when the universe was about half its current age. Recent advances from the James Webb Space Telescope (JWST), leveraging its near-infrared capabilities up to 2025, have enhanced redshift detections of galaxies at z=2–5 by resolving their rest-frame optical morphologies through deep imaging surveys.^[55] For instance, NIRCam observations in programs like MIDIS have uncovered disk-like and clumpy structures in these high-redshift galaxies, indicating rapid morphological evolution driven by mergers and star formation during cosmic noon.^[55] These detections connect redshift measurements to the assembly of stellar populations, illuminating galaxy evolution in the early universe. In interpreting these extragalactic redshifts, the luminosity distance-redshift relation is fundamental for estimating distances in a flat universe, given by

d_L = (1 + z)^2 d_p,

where

d_p

is the proper distance and the factor accounts for photon dilution and time dilation effects. This relation underpins the conversion of observed fluxes to intrinsic luminosities, enabling the mapping of redshift to cosmic expansion and the inference of evolutionary timelines for distant structures.

High-Redshift Records

High-redshift records refer to the most distant astrophysical objects confirmed through spectroscopic measurements, providing direct probes of the early universe. These records have advanced rapidly with the advent of the James Webb Space Telescope (JWST), surpassing previous limits set by the Hubble Space Telescope. JWST's primary capability to observe in the infrared spectrum enables it to detect light from these distant galaxies that has been redshifted from ultraviolet and visible wavelengths into the infrared due to the expansion of the universe, whereas the Hubble Space Telescope, optimized for visible and ultraviolet light, was limited in probing such early epochs.^[56] The redshift values indicate lookback times exceeding 13 billion years, corresponding to cosmic epochs within 300-500 million years after the Big Bang. One of the landmark discoveries is GN-z11, a compact star-forming galaxy initially identified by Hubble in 2016 with a photometric redshift estimate of z ≈ 11. Spectroscopic confirmation refined this to z = 10.603 ± 0.001 using JWST's NIRSpec instrument in 2023, establishing it as a key high-redshift benchmark from the pre-JWST era. This galaxy, observed when the universe was about 400 million years old, exhibits strong Lyman-alpha emission and a young stellar population, highlighting early galaxy assembly. JWST follow-up revealed a supermassive black hole candidate in its core, further emphasizing its role in probing primordial conditions.^[57] The JWST era has shattered these records, with JADES-GS-z14-0 confirmed at z = 14.32 +0.08/-0.20 in 2024 through NIRSpec spectroscopy detecting Lyman-alpha emission redward of the Lyman break. This luminous galaxy, spanning over 1,600 light-years and formed just 290 million years after the [Big Bang](/page/Big Bang), challenges models of rapid early star formation due to its unexpected size and brightness. It was identified via the JADES survey's dropout technique, selecting candidates with red colors indicating Lyman break dropout into the infrared.^[58] In 2025, JWST broke this record again with MoM-z14 at z = 14.44, spectroscopically confirmed via broad Lyman-alpha emission, dating to approximately 280 million years post-Big Bang. This "cosmic miracle" galaxy is remarkably luminous for its epoch, with no strong damping wing in its spectrum suggesting partial ionization in its vicinity during the cosmic dawn. Discovered through targeted NIRCam imaging and spectroscopy, it underscores JWST's ability to resolve fine details in the reionization era.^[59]^[60] Notable 2024-2025 updates include the confirmation of a massive quiescent galaxy at z ≈ 7.3 by the RUBIES survey, the highest-redshift spectroscopically verified example of a galaxy with suppressed star formation as of November 2025, with a stellar mass of ~10^{11} solar masses observed via JWST/NIRSpec and residing in an overdense environment, implying efficient quenching mechanisms operated early in cosmic history. Meanwhile, the GLIMPSE survey has identified potential candidates at z > 15, such as two objects at 15.7 < z < 16.4 behind the Abell S1063 cluster, selected via gravitational lensing and Lyman-break criteria; spectroscopic follow-up is pending to confirm these frontier detections.^[61]^[62] These records trace a timeline of discovery: early high-redshift quasars at z ≈ 7 emerged in the 2000s via ground-based surveys like SDSS, such as J1148+5251 at z = 6.42 in 2003. Hubble pushed galaxy records to z ≈ 10 by the 2010s, culminating in GN-z11. JWST's 2022-2025 observations have extended this to z > 14, revealing an abundance of massive galaxies that probe the reionization era and challenge standard formation models by indicating faster growth than predicted. Confirming such high-redshift objects faces challenges, including the Lyman break shifting ultraviolet emission into the near-infrared, necessitating sensitive IR spectroscopy to detect faint lines like Lyman-alpha amid cosmic expansion effects. Dropout techniques, relying on color selections where flux drops sharply blueward of the Lyman limit, enable efficient candidate identification but require spectroscopic verification to rule out lower-redshift interlopers. These records imply that reionization began earlier than thought, with early massive galaxies contributing significantly to ionizing photons and potentially requiring revisions to galaxy evolution models.^[59]

Redshift Surveys

Redshift surveys systematically measure the redshifts of large numbers of galaxies and other objects to map the three-dimensional distribution of matter in the universe, enabling studies of large-scale cosmic structure.^[63] These surveys typically combine photometric pre-selection with spectroscopic follow-up to achieve high-precision redshift estimates, covering vast sky areas to sample volumes exceeding hundreds of cubic gigaparsecs. By analyzing clustering patterns in these maps, researchers probe the underlying cosmology without relying on individual object luminosities.^[64] Key examples include the Sloan Digital Sky Survey (SDSS), which has cataloged over 10^6 galaxies primarily at redshifts z < 0.4 through its main galaxy sample and luminous red galaxy selections, providing foundational data on low-redshift structure. The Dark Energy Spectroscopic Instrument (DESI) survey, operational in the 2020s, targets approximately 40 million objects including galaxies up to z ≈ 1, using a fiber-fed spectrograph on the Mayall 4-m telescope to measure baryon acoustic oscillations (BAO) and redshift-space distortions across cosmic time. Launched in 2023, the Euclid space mission extends spectroscopic capabilities to z ≈ 2 for tens of millions of galaxies via its near-infrared spectrometer, complementing ground-based efforts with wide-field imaging over 15,000 square degrees. A primary science goal of these surveys is detecting baryon acoustic oscillations (BAO), which serve as a standard ruler imprinted in the galaxy distribution at a comoving scale of roughly 150 Mpc, calibrated from cosmic microwave background measurements. BAO measurements from z ≈ 0.5 to 2.5 constrain the expansion history H(z) by comparing observed angular and radial scales to theoretical predictions, offering a model-independent probe of dark energy evolution. Redshift surveys also quantify redshift-space distortions (RSD), arising from galaxy peculiar velocities that elongate structures along the line of sight, allowing measurement of the growth rate parameter fσ_8, where f is the logarithmic derivative of the growth factor and σ_8 normalizes matter fluctuations on 8 h^{-1} Mpc scales. These RSD analyses, modeled via linear perturbation theory on large scales, test gravity on cosmological scales and distinguish between dark energy and modified gravity scenarios.^[65] As of 2025, DESI's Year 2 data release (DR2) has provided enhanced BAO constraints that partially mitigate the Hubble tension by indicating a redshift-evolving expansion rate consistent with early-universe measurements from the cosmic microwave background, reducing discrepancies with local distance ladder estimates. Survey data products include detailed 3D galaxy maps that visualize filamentary structures and voids, alongside computed power spectra that quantify clustering amplitude and BAO features for direct comparison with ΛCDM predictions. These outputs, publicly released with covariance matrices, facilitate community tests of cosmological models and enable cross-correlations with other datasets.

Blueshift Effects

Blueshift is the counterpart to redshift, characterized by a negative value of the redshift parameter (z < 0), where the observed wavelength of light is shorter than the emitted wavelength due to compression from an approaching source or light descending into a gravitational potential well.^[66] In astronomical contexts, the most common cause of blueshift is the relativistic Doppler effect from sources moving toward the observer. The formula for the redshift parameter in this case is

z = \sqrt{\frac{1 - \beta}{1 + \beta}} - 1

z=1+β1−β

−1, where $\beta = v/c$ and $v$ is the radial speed toward the observer (positive for approach). For non-relativistic speeds ( $v \ll c$ ), this simplifies to $z \approx -v/c$ . A well-known example is the Andromeda Galaxy (M31), which displays an observed blueshift of z ≈ -0.001 (heliocentric radial velocity ≈ -300 km/s), reflecting its approach toward the Milky Way at a relative velocity of approximately 110 km/s, driven by gravitational interactions within the Local Group.^[35]^[67] Gravitational blueshift occurs when photons gain energy by falling toward a massive body, increasing their frequency as they enter a deeper gravitational potential. In the weak-field limit, the shift is approximated by $z \approx -\frac{GM}{c^2 r}$ , where $G$ is the gravitational constant, $M$ is the mass, $c$ is the speed of light, and $r$ is the radial distance. This effect is the inverse of the gravitational redshift demonstrated in the Pound-Rebka experiment (1959), where gamma rays transmitted downward in Earth's gravitational field experienced a measurable blueshift of about $2.5 \times 10^{-15}$ over a 22.6 m height. Astrophysically, such blueshifts are evident in spectra of accreting material around black holes or neutron stars, where infalling gas lines appear shifted to shorter wavelengths. Cosmological blueshifts are uncommon beyond local scales owing to the universe's overall expansion but arise from peculiar velocities or local overdensities that counteract the Hubble flow. These include galaxies with motions directed toward us due to cluster infall, such as Messier 98 (M98) in the Virgo Cluster, which shows a blueshift of $z \approx -0.0005$ (corresponding to -150 km/s) from its orbital dynamics within the cluster potential. Similarly, infalling cool gas in galaxy clusters often produces blueshifted absorption features in quasar sightlines, revealing cold streams (T < 10^4 K) moving at velocities up to several hundred km/s toward the cluster center, as observed in systems like the Perseus Cluster.^[68]^[69]

Non-Physical Mimics

In astronomical observations, radiative transfer effects through interstellar dust can produce apparent reddening of celestial objects, mimicking aspects of redshift in broadband photometry by preferentially attenuating shorter wavelengths. Dust grains scatter and absorb blue light more efficiently than red light, following extinction curves where the optical depth τ_λ scales approximately as τ_λ ∝ λ^{-1} in the optical regime, leading to a color excess E(B-V) that tilts the continuum spectrum redward without shifting emission lines. This phenomenon, known as interstellar reddening, arises from the size distribution of dust particles comparable to optical wavelengths, resulting in higher extinction A_λ at shorter λ. For instance, in the Milky Way, the standard extinction law parameterizes this as A_λ / A_V ≈ a(λ) + b(λ)/R_V, where R_V ≈ 3.1 for diffuse clouds, emphasizing the wavelength-dependent absorption that favors red light transmission. Instrumental effects in spectrographs can artifactually shift spectral lines, simulating redshift if calibration is imprecise. CCD fringing, caused by thin-film interference in back-illuminated detectors at wavelengths >8000 Å, produces periodic patterns that distort continuum and line profiles, complicating redshift determinations for high-z galaxies where only strong emission lines like Hα are reliable. Similarly, grating dispersion errors from misalignment, temperature drifts, or imperfect ruling can introduce wavelength scale inaccuracies of Δλ/λ ~ 10^{-4} (equivalent to ~20 km/s velocity error), leading to systematic offsets in measured z if not corrected via nightly calibrations with arc lamps. These artifacts are particularly problematic in long-slit or multi-object spectrographs without stable etalons.^[70]^[71] Atmospheric dispersion in ground-based telescopes causes differential refraction, bending light rays by varying amounts across wavelengths due to the air's dispersive index n(λ), displacing images by up to ~0.3 arcsec over wide fields at non-zenith angles. This chromatic effect elongates spectra along the parallactic angle, potentially shifting line centroids in slit spectroscopy if the slit is misaligned, mimicking small z errors (Δz ~ 0.001) for unresolved sources; field differential refraction adds achromatic offsets varying quadratically with field angle. Corrections involve atmospheric dispersion compensators (ADCs) or slit orientation along the parallactic direction, reducing distortions to <15% flux loss.^[72] To distinguish non-physical mimics from true redshift, multi-wavelength spectroscopy verifies consistent line shifts across bands, as dust reddening affects continuum slopes without displacing lines, while instrumental or atmospheric artifacts fail to produce uniform velocity offsets. Polarimetry further aids in identifying dust contributions, detecting linearly polarized thermal emission from aligned grains (P ~ 0.5-1% at sub-mm wavelengths), which is absent in pure redshift scenarios and confirms magnetic field orientations in the interstellar medium. These methods, combining polarimetric and spectrophotometric data, effectively rule out artifacts by isolating dynamical signals.^[73]

Cosmological Implications

Expansion and Hubble Constant

The observed redshift of distant galaxies provides a direct measure of the universe's expansion, with the Hubble constant

H_0

quantifying the current expansion rate as the proportionality between recession velocity and distance, typically expressed in km/s/Mpc.^[74] Local measurements using the cosmic distance ladder, anchored by Cepheid variables and calibrated with Type Ia supernovae at redshifts

z \approx 0.01

1.5

, yield

H_0 \approx 73

km/s/Mpc from the SH0ES collaboration, which employs Hubble Space Telescope and James Webb Space Telescope observations to refine supernova distances.^[75] In contrast, early-universe inferences from cosmic microwave background (CMB) data by the Planck satellite give

H_0 \approx 67

km/s/Mpc, highlighting a tension exceeding 5σ that arises from discrepancies between local (late-time) and CMB (early-time) probes.^[76] This Hubble tension challenges the standard ΛCDM model and motivates investigations into systematic errors or new physics, such as evolving dark energy. In 2025, the Dark Energy Spectroscopic Instrument (DESI) released baryon acoustic oscillation (BAO) measurements from its second data release (DR2) in March, analyzing over 14 million galaxies and quasars, which strengthen hints of dark energy evolution at 4.2σ significance, suggesting its density may weaken over time rather than remaining constant.^[77] Further, November 2025 studies incorporating corrected supernova data with BAO and CMB analyses indicate the universe's expansion may have transitioned to deceleration in the present epoch, potentially hinting at a future "Big Crunch" scenario where expansion reverses, though these findings remain preliminary and require confirmation.^[78] The Friedmann equation governs this expansion within general relativity, relating the Hubble parameter

H = \dot{a}/a

(where

a

is the scale factor) to the universe's energy content:

\left( \frac{\dot{a}}{a} \right)^2 = H^2 = \frac{8\pi G}{3} \rho - \frac{k c^2}{a^2} + \frac{\Lambda}{3},

where

\rho

is the total energy density,

k

the curvature parameter,

G

the gravitational constant,

c

the speed of light, and

\Lambda

the cosmological constant.^[79] Resolving the

H_0

tension could profoundly impact ΛCDM, potentially requiring modifications to dark energy dynamics or early-universe physics to reconcile local and global measurements.^[80]

Galaxy Evolution Insights

Redshift measurements provide a direct measure of lookback time, enabling astronomers to reconstruct the evolutionary timeline of galaxies over cosmic history. The lookback time

t_L(z)

to an object at redshift

z

is calculated as the integral

t_L(z) = \int_0^z \frac{dz'}{H(z')(1 + z')},

where

H(z')

is the Hubble parameter at redshift

z'

.^[81] In the standard

\Lambda

CDM cosmology with current parameters (

H_0 \approx 70

km/s/Mpc,

\Omega_m \approx 0.3

), this yields approximately 13 Gyr at

z = 10

, allowing observations to probe conditions within ~500 Myr of the Big Bang.^[82] Such timescales reveal how galaxies assembled their stellar mass and evolved chemically across the universe's 13.8 Gyr history. The star formation history of the universe, traced via redshifted ultraviolet and infrared emissions, exhibits a peak in the cosmic star formation rate density at

z \approx 2

, corresponding to ~3.5 Gyr after the Big Bang.^[83] At this epoch, galaxies underwent rapid assembly, with ~25% of the present-day stellar mass density formed before the peak and another ~25% since

z \approx 0.7

.^[84] James Webb Space Telescope (JWST) observations from 2024–2025 of galaxies at

z > 6

indicate bursty star formation histories, characterized by intense, episodic bursts rather than steady accretion, leading to elevated nitrogen-to-oxygen (N/O) abundance ratios that exceed solar values.^[85] These high N/O ratios arise from rapid enrichment by core-collapse supernovae during bursts, combined with differential galactic winds that preferentially eject oxygen-rich material, as reproduced in chemical evolution models for galaxies of

10^9

–

10^{10} \, M_\odot

.^[86] The THESAN radiation-hydrodynamic simulations corroborate this, simulating cycles of bursty formation and quenching at high redshift, where star formation efficiencies vary dramatically with ionized bubble sizes during reionization.^[87] Quenching mechanisms, which halt star formation in massive galaxies, are illuminated by JWST discoveries of early quiescent systems. A prime example is the spectroscopically confirmed galaxy RUBIES-EGS-QG-1 at

z = 4.9

, with a stellar mass of

9.9 \times 10^{10} \, M_\odot

assembled in a short burst peaking at ~870

M_\odot

^{-1}

over

\Delta t \approx 180

Myr, followed by quenching within ~100 Myr.^[88] This rapid evolution challenges semi-analytic and hydrodynamical models like TNG300 and FLARES, which predict slower mass growth and lower number densities (

n \approx 5 \times 10^{-8}

Mpc

^{-3}

) compared to observations (

n \approx 4.5 \times 10^{-6}

Mpc

^{-3}

).^[88] Such findings suggest enhanced feedback from active galactic nuclei or mergers accelerated quenching, addressing gaps in understanding massive galaxy formation at

z > 4

. During reionization, Lyman-alpha emitters at

z = 6

–9 trace the evolving neutral hydrogen fraction in the intergalactic medium. The visibility of Lyman-alpha emission, resonant with neutral hydrogen, diminishes at higher redshifts as the neutral fraction increases, with the emitter fraction dropping monotonically from ~30% at

z \sim 6

to <10% at

z \sim 8

–13.^[89] This decline reflects the patchy ionization state, where emitters probe ionized bubbles around galaxies, providing constraints on the reionization timeline and sources.^[90] JWST's mid-infrared spectroscopy has revolutionized insights into high-redshift chemistry and dynamics, revealing underemphasized roles of mergers in galaxy evolution. At

z > 2

, frequent mergers drive the growth of massive black holes (MBHs), with 2025 studies predicting ~10 detectable LISA gravitational wave events per year from MBH binaries at

z \gtrsim 10

, involving seeds of

10^3

–

10^5 \, M_\odot

.^[91] These signals align with JWST observations of overmassive MBHs in early galaxies, supporting hierarchical merger channels over direct collapse.^[91] Combined with chemical signatures like high N/O ratios, such data highlight mergers' contributions to bursty evolution and rapid enrichment, filling gaps in models of cosmic history.^[85]

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