View source for Redshift

{{short description|Change in wavelength of light}}
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[[File:Redshift.svg|thumb|upright|[[Spectral line|Absorption lines]] in the [[visible spectrum]] of a [[supercluster]] of distant galaxies (right), as compared to absorption lines in the visible spectrum of the [[Sun]] (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).]]
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In [[physics]], a '''redshift''' is an increase in the [[wavelength]], or equivalently, a decrease in the [[frequency]], of [[electromagnetic radiation]] (such as [[light]]). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a [[#Blueshift|blueshift]].

Three forms of redshift occur in [[astronomy]] and [[cosmology]]: [[Doppler effect|Doppler]] redshifts due to the relative motions of radiation sources, [[gravitational redshift]] as radiation escapes from [[gravitational potential]]s, and cosmological redshifts caused by the [[expansion of the universe|universe expanding]]. In [[astronomy]], the value of a redshift is often denoted by the letter {{math|''z''}}, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio {{math|1 + ''z''}} (which is greater than 1 for redshifts and less than 1 for blueshifts). Automated astronomical redshift surveys are an important tool for learning about the large-scale structure of the universe. Redshift and blueshift can also be related to [[photon energy]] and, via [[Planck's law]], to a corresponding [[blackbody temperature]].

Examples of strong redshifting are a [[gamma ray]] perceived as an [[X-ray]], or initially visible light perceived as [[radio wave]]s. The initial 3000 [[kelvin]] (K) radiation from the [[Big Bang]] has redshifted far down to become the 3{{nbsp}}K [[cosmic microwave background]]. Subtler redshifts are seen in the [[astronomical spectroscopy|spectroscopic]] observations of [[astronomical object]]s, and are used in terrestrial technologies such as [[Doppler radar]] and [[radar gun]]s. 
[[Gravitational wave]]s, which also travel at [[Speed of light|the speed of light]], are subject to the same redshift phenomena.<ref>{{cite journal | title=Detectability of primordial black hole binaries at high redshift | last=Ding | first=Qianhang | journal=Physical Review D | volume=104 | issue=4 | at=id. 043527 | date=August 2021 | article-number=043527 | doi=10.1103/PhysRevD.104.043527 | arxiv=2011.13643 | bibcode=2021PhRvD.104d3527D }}</ref>

Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including [[scattering]] and [[physical optics|optical effects]]; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such.

==Concept==
[[File:High-redshift galaxy candidates in the Hubble Ultra Deep Field 2012.jpg|thumb|High-redshift galaxy candidates in the [[Hubble Ultra Deep Field]], 2012<ref>{{cite news|title=Hubble census finds galaxies at redshifts 9 to 12|url=https://esahubble.org/news/heic1219/|access-date=13 December 2012|newspaper=ESA/Hubble Press Release}}</ref> ]]

Using a telescope and a [[spectrometer]], the variation in intensity of star light with frequency can be measured. The resulting spectrum can be compared to the spectrum from hot gases expected in stars, such as [[hydrogen]], in a laboratory on Earth. As illustrated with the idealised spectrum in the top-right, to determine the redshift, features in the two spectra such as [[spectral line|absorption lines]], [[spectral line|emission lines]], or other variations in light intensity<!--Don't link to disambiguation page--> may be shifted.

Redshift (and blueshift) may be characterised by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a [[dimensionless quantity]] called {{math|''z''}}. If {{math|''λ''}} represents wavelength and {{math|''f''}} represents frequency (note, {{math|''λf'' {{=}} ''c''}} where {{math|''c''}} is the [[speed of light]]), then {{math|''z''}} is defined by the equations:<ref>{{cite web
 | title=Extragalactic Redshifts
 | first=John
 | last=Huchra
 | publisher=Harvard-Smithsonian Center for Astrophysics
 | website=NASA/IPAC Extragalactic Database
 | url=http://ned.ipac.caltech.edu/help/zdef.html
 | access-date=2023-03-16
 | archive-date=2013-12-22
 | archive-url=https://web.archive.org/web/20131222052715/http://ned.ipac.caltech.edu/help/zdef.html}}</ref>

{| class="wikitable" style="margin:auto;"
|+ Calculation of redshift, <math>z</math>
!Based on wavelength!!Based on frequency
|- align=center
| <math>z = \frac{\lambda_{\mathrm{obsv}} - \lambda_{\mathrm{emit}}}{\lambda_{\mathrm{emit}}}</math>
| <math>z = \frac{f_{\mathrm{emit}} - f_{\mathrm{obsv}}}{f_{\mathrm{obsv}}}</math>
|- align=center
| <math>1+z = \frac{\lambda_{\mathrm{obsv}}}{\lambda_{\mathrm{emit}}}</math>
| <math>1+z = \frac{f_{\mathrm{emit}}}{f_{\mathrm{obsv}}}</math>
|}

[[Doppler effect]] blueshifts ({{math|''z'' < 0}}) are associated with objects approaching (moving closer to) the observer with the light shifting to greater [[energy|energies]]. Conversely, Doppler effect redshifts ({{math|''z'' > 0}}) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker [[gravitational field]] as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.

==History==

The history of the subject began in the 19th century, with the development of [[classical mechanics|classical wave mechanics]] and the exploration of phenomena which are associated with the [[Doppler effect]]. The effect is named after the Austrian mathematician [[Christian Doppler]], who offered the first known physical explanation for the phenomenon in 1842.<ref>
{{cite book
 |last=Doppler | first=Christian
 |date=1846
 |title=Beiträge zur Fixsternenkunde
 |language=de
 |trans-title=Contributions to fixed-star science
 |location=Prague |publisher=G. Haase Söhne
 |bibcode=1846befi.book.....D
 |volume=69
}}</ref><ref name=Becker-2011>{{Cite book |last=Becker |first=Barbara J. |url=https://www.cambridge.org/core/product/identifier/9780511751417/type/book |title=Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy |date=2011-02-17 |publisher=Cambridge University Press |isbn=978-1-107-00229-6 |edition=1 |doi=10.1017/cbo9780511751417}}</ref>{{rp|107}} In 1845, the hypothesis was tested and confirmed for [[sound wave]]s by the Dutch scientist [[C. H. D. Buys Ballot|Christophorus Buys Ballot]].<ref>
{{cite book
 |last=Maulik | first=Dev
 |chapter=Doppler Sonography: A Brief History
 |chapter-url=https://books.google.com/books?id=HedeGJms0n4C&q=%22Ballot%22&pg=PA3
 |editor1-last=Maulik | editor1-first=Dev
 |editor2-last=Zalud | editor2-first=Ivica
 |date=2005
 |title=Doppler Ultrasound in Obstetrics And Gynecology
 |url= https://www.springer.com/west/home/medicine/gynecology?SGWID=4-10066-22-46625046-0
 |isbn=978-3-540-23088-5
 |publisher=Springer
 }}</ref> Doppler correctly predicted that the phenomenon would apply to all [[wave]]s and, in particular, suggested that the varying [[Stellar classification#Conventional colour description|colors of stars]] could be attributed to their motion with respect to the Earth.<ref>
{{cite web
 |last1=O'Connor | first1=John J.
 |last2=Robertson | first2=Edmund F.
 |date=1998
 |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Doppler.html
 |title=Christian Andreas Doppler
 |work=[[MacTutor History of Mathematics archive]]
 |publisher=[[University of St Andrews]]
}}</ref>

Unaware of Doppler's work, French physicist [[Hippolyte Fizeau]] suggested in 1848 that a shift in [[spectral line]]s from stars might be used to measure their motion relative to Earth.<ref name=Becker-2011/>{{rp|109}} In 1850, [[François-Napoléon-Marie Moigno]] analysed both Doppler's and Fizeau's ideas in a publication read by both [[James Clerk Maxwell]] and [[William Huggins]], who initially stuck to the idea that the color of stars related to their chemistry, however by 1868, Huggins was the first to determine the velocity of a star moving away from the Earth by the analysis of spectral shifts.<ref name=Huggins>
{{cite journal
 |last=Huggins | first=William
 |date=1868
 |title=Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II
 |journal=[[Philosophical Transactions of the Royal Society of London]]
 |volume= 158 |pages=529–564
 |bibcode=1868RSPT..158..529H
 |doi=10.1098/rstl.1868.0022
}}</ref><ref name=Becker-2011/>{{rp|111}}

In 1871, optical redshift was confirmed when the phenomenon was observed in [[Fraunhofer lines]], using solar rotation, about 0.1 Å in the red.<ref name="Nolte">{{cite journal |author1-link=David D. Nolte |last1=Nolte |first1=David D. |title=The fall and rise of the Doppler effect |journal=Physics Today |date=1 March 2020 |volume=73 |issue=3 |pages=30–35 |doi=10.1063/PT.3.4429 |doi-access=free |bibcode=2020PhT....73c..30N }}</ref> In 1887, [[Hermann Carl Vogel]] and [[Julius Scheiner]] discovered the "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth.<ref>{{cite book|last=Pannekoek|first=A.|title=A History of Astronomy |date=1961|publisher=Interscience|page=451|url=https://archive.org/details/historyofastrono0000pann/page/450/mode/2up?view=theater}}</ref> In 1901, [[Aristarkh Belopolsky]] verified optical redshift in the laboratory using a system of rotating mirrors.<ref>
{{cite journal
 |last=Bélopolsky | first=A.
 |date=1901
 |bibcode=1901ApJ....13...15B
 |title=On an Apparatus for the Laboratory Demonstration of the Doppler-Fizeau Principle
 |journal=[[Astrophysical Journal]]
 |volume=13 |page=15
 |doi=10.1086/140786
|doi-access=free
 }}</ref><ref name="Nolte"/>

Beginning with observations in 1912, [[Vesto Slipher]] discovered that the [[Andromeda Galaxy]] had a blue shift, indicating that it was moving towards the Earth.<ref name="SmithInKragh-2019">{{Cite book |last=Robert |first=Smith |title=The Oxford handbook of the history of modern cosmology |date=2019 |publisher=Oxford University Press |isbn=978-0-19-881766-6 |editor-last=Kragh |editor-first=Helge |chapter=Observations and the universe |oclc=1052868704 |editor-last2=Longair |editor-first2=Malcolm S.}}</ref> Slipher first reported his measurement in the inaugural volume of the ''[[Lowell Observatory]] Bulletin''.<ref>
{{cite journal
 |last=Slipher | first=Vesto
 |date=1912
 |title=The radial velocity of the Andromeda Nebula
 |journal=[[Lowell Observatory Bulletin]]
 |volume=1 |issue=8
 |pages=2.56–2.57
 |bibcode=1913LowOB...2...56S
 |quote=The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it
}}</ref> Three years later, he wrote a review in the journal ''[[Popular Astronomy (US magazine)|Popular Astronomy]]''.<ref name=Slipher>
{{cite journal
 |last=Slipher | first=Vesto
 |title=Spectrographic Observations of Nebulae
 |url=https://archive.org/details/sim_popular-astronomy_1915-01_23_1/page/20 |journal=[[Popular Astronomy (US magazine)|Popular Astronomy]]
 |volume=23 |pages=21–24 |date=1915
 |bibcode=1915PA.....23...21S
}}</ref> In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km[/s] showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well."<ref name=Slipher /> Slipher reported the velocities for 15 [[Spiral galaxy#Spiral nebula|spiral nebulae]] spread across the entire [[celestial sphere]], all but three having observable "positive" (that is recessional) velocities.<ref name="SmithInKragh-2019"/>

Until 1923 the nature of the nebulae was unclear. By that year [[Edwin Hubble]] had established that these were [[galaxy|galaxies]] and worked out a procedure to measure distance based on the period-luminosity relation of variable [[Cepheids]] stars. This made it possible to test a prediction by [[Willem de Sitter]] in 1917 that redshift would be correlated with distance. In 1929 Hubble combined his distance estimates with redshift data from Slipher's reports and measurements by [[Milton Humason]] to report an approximate relationship between the redshift and distance, a result now called [[Hubble's law]].<ref name="SmithInKragh-2019"/>{{rp|64}}<ref>
{{cite journal
 |doi=10.1073/pnas.15.3.168
 |last=Hubble |first=Edwin
 |date=1929
 |bibcode=1929PNAS...15..168H
 |title=A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae
 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
 |volume=15 |issue=3 |pages=168–173
 |pmid=16577160
 |pmc=522427
 |doi-access=free
}}</ref><ref>{{Cite web|url=https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/online_edition/1929/expanding.html|title=Universe is Expanding|date=2017-12-08|access-date=2023-09-06 |publisher=Goddard Space Flight Center}}</ref>

Theories relating to the redshift-distance relation also evolved during the 1920s. The solution to the equations of general relativity described by de Sitter contained no matter, but in 1922 [[Alexander Friedmann]] derived dynamic solutions, now called the [[Friedmann equations]], based on frictionless fluid models.<ref>{{cite journal
 |last=Friedman |first=A. A.
 |date=1922
 |title=Über die Krümmung des Raumes
 |journal=[[Zeitschrift für Physik]]
 |volume=10
 |issue=1 |pages=377–386
 |doi=10.1007/BF01332580
|bibcode = 1922ZPhy...10..377F |s2cid=125190902
 }} English translation in {{cite journal |title=On the Curvature of Space|doi=10.1023/A:1026751225741 |last=Friedman |first=A. |date=1999  |journal=[[General Relativity and Gravitation]] |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F|s2cid=122950995 }})</ref> Independently [[Georges Lemaître]] derived similar equations in 1927 and his analysis became widely known around the time of Hubble's key publication.<ref name="SmithInKragh-2019"/>{{rp|77}}

By early 1930 the combination of the redshift measurements and theoretical models established a major breakthrough in the new science of cosmology: the universe had a history and its expansion could be investigated with physical models backed up with observational astronomy.<ref name="SmithInKragh-2019"/>{{rp|99}}

When cosmological redshifts were first discovered, [[Fritz Zwicky]] proposed an effect known as [[tired light]].  However this model has largely been ruled out by timescale stretch observations in [[type Ia supernovae]].<ref>{{cite journal | title=Timescale Stretch Parameterization of Type Ia Supernova B-Band Lightcurves | first1=G. | last1=Goldhaber | first2=D. E. | last2=Groom | first3=A. | last3=Kim | first4=G. | last4=Aldering | first5=P. | last5=Astier | first6=A. | last6=Conley | first7=S. E. | last7=Deustua | first8=R. | last8=Ellis | first9=S. | last9=Fabbro | first10=A. S. | last10=Fruchter | first11=A. | last11=Goobar | first12=I. | last12=Hook | first13=M. | last13=Irwin | first14=M. | last14=Kim | first15=R. A. | last15=Knop | first16=C. | last16=Lidman | first17=R. | last17=McMahon | first18=P. E. | last18=Nugent | first19=R. | last19=Pain | first20=N. | last20=Panagia | first21=C. R. | last21=Pennypacker | first22=S. | last22=Perlmutter | first23=P. | last23=Ruiz-Lapuente | first24=B. | last24=Schaefe | first25=N. A. | last25=Walton | first26=T. | last26=York |display-authors=6 | year=2001 | journal=Astrophysical Journal | volume=558 | issue=1 | pages=359–386 | doi=10.1086/322460 | arxiv=astro-ph/0104382 | bibcode=2001ApJ...558..359G | s2cid=17237531| doi-access=free }}</ref>

[[Arthur Eddington]] used the term "red shift" as early as 1923, which is the oldest example of the term reported by the ''[[Oxford English Dictionary]]''.<ref>{{Cite book |last=Eddington |first=Arthur Stanley |url=https://books.google.com/books?id=errkj2WXGzIC&pg=PA164 |title=The Mathematical Theory of Relativity |date=1923 |publisher=The University Press |page=164 |author-link=Arthur Eddington}}</ref><ref>{{Cite OED|term=redshift|id=160477|access-date=2023-03-17}}</ref> Willem de Sitter used the single-word version ''redshift'' in 1934.<ref>
{{cite journal
 |last=de Sitter | first=W.
 |date=1934
 |title=On distance, magnitude, and related quantities in an expanding universe
 |journal=[[Bulletin of the Astronomical Institutes of the Netherlands]]
 |volume=7 |page=205
 |bibcode=1934BAN.....7..205D
 |quote=It thus becomes urgent to investigate the effect of the redshift and of the metric of the universe on the apparent magnitude and observed numbers of nebulae of given magnitude
}}</ref>

In the 1960s the discovery of [[quasars]], which appear as very blue point sources and thus were initially thought to be unusual stars, led to the idea that they were as bright as they were because they were closer than their redshift data indicated. A flurry of theoretical and observational work concluded that these objects were very powerful but distant astronomical objects.<ref name="SmithInKragh-2019"/>{{rp|261}}

== Physical origins ==
Redshifts are differences between two wavelength measurements and wavelengths are a property of both the photons and the measuring equipment. Thus redshifts characterise differences between two measurement locations. These differences are commonly organised in three groups, attributed to relative motion between the source and the observer, to the expansion of the universe, and to gravity.<ref>{{cite journal |last1=Lewis |first1=Geraint F. |title=On The Relativity of Redshifts: Does Space Really 'Expand'? |journal=Australian Physics |date=2016 |volume=53 |page=95 |arxiv=1605.08634 }}</ref> The following sections explain these groups.

===Doppler effect===
{{Main|Doppler effect|Relativistic Doppler effect}}
[[Image:Suzredshift.gif|thumb|[[Doppler effect]], yellow (c.&nbsp;575 [[Nanometre|nm]] wavelength) ball appears greenish (blueshift to c.&nbsp;565 nm wavelength) approaching observer, turns [[Orange (colour)|orange]] (redshift to c.&nbsp;585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in colour, the object would have to be travelling at approximately 5,200 [[Metre per second|km/s]], or about 32 times faster than the speed record for the [[Parker Solar Probe|fastest space probe]].]]
[[File:Redshift blueshift.svg|thumb|Redshift and blueshift]]

If a source of the light is moving away from an observer, then redshift ({{math|''z'' > 0}}) occurs; if the source moves towards the observer, then [[blueshift]] ({{math|''z'' < 0}}) occurs. This is true for all electromagnetic waves and is explained by the [[Doppler effect]]. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with [[velocity]] {{math|''v''}}, which is much less than the speed of light ({{math|''v'' ≪ ''c''}}), the redshift is given by

<math display="block">z \approx \frac{v}{c}</math>

where {{math|''c''}} is the [[speed of light]] (since <math>\gamma \approx 1</math>). In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the [[relativistic Doppler effect]]. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the [[time dilation]] of [[special relativity]] which can be corrected for by introducing the [[Lorentz factor]] {{math|''γ''}} into the classical Doppler formula as follows (for motion solely in the line of sight):

<math display="block">1 + z = \left(1 + \frac{v}{c}\right) \gamma.</math>

This phenomenon was first observed in a 1938 experiment performed by [[Herbert E. Ives]] and G. R. Stilwell, called the [[Ives–Stilwell experiment]].<ref>{{cite journal | last1 = Ives | first1 = H. | last2 = Stilwell | first2 = G. | year = 1938 | title = An Experimental study of the rate of a moving atomic clock | journal = Journal of the Optical Society of America | volume = 28 | issue = 7| pages = 215–226 | doi=10.1364/josa.28.000215 | bibcode = 1938JOSA...28..215I}}</ref>

Since the Lorentz factor is dependent only on the [[magnitude (mathematics)|magnitude]] of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the [[scalar resolute|projection]] of the movement of the source into the [[Line-of-sight propagation|line-of-sight]] which yields different results for different orientations. If {{math|''θ''}} is the angle between the direction of relative motion and the direction of emission in the observer's frame<ref>{{cite book|last=Freund|first=Jurgen|title=Special Relativity for Beginners|date=2008|publisher=World Scientific|page=120|isbn=978-981-277-160-5}}</ref> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

<math display="block">1+ z = \frac{1 + v \cos (\theta)/c}{\sqrt{1-v^2/c^2}}</math>

and for motion solely in the line of sight ({{math|''θ'' {{=}} 0°}}), this equation reduces to:

<math display="block">1 + z = \sqrt{\frac{1+v/c}{1-v/c}}</math>

For the special case that the light is moving at [[right angle]] ({{math|''θ'' {{=}} 90°}}) to the direction of relative motion in the observer's frame,<ref>{{cite book|last=Ditchburn|first=R. |title=Light|date=1991|publisher=Dover|page=329|isbn=978-0-12-218101-6}}</ref> the relativistic redshift is known as the [[Relativistic Doppler effect|transverse redshift]], and a redshift:

<math display="block">1 + z = \frac{1}{\sqrt{1-v^2/c^2}}</math>

is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.<ref>[http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm "Photons, Relativity, Doppler shift"]. {{Webarchive|url=https://web.archive.org/web/20060827063802/http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm |date=2006-08-27 }}. University of Queensland.
</ref>

===Cosmological <span class="anchor" id="Cosmological"></span>===
{{Main|Expansion of the universe}}

The observations of increasing redshifts from more and more distant galaxies can be modelled assuming a [[cosmological principle|homogeneous and isotropic universe]] combined with [[general relativity]]. This cosmological redshift can be written as a function of {{math|''a''}}, the time-dependent cosmic [[Scale factor (cosmology)|scale factor]]:<ref>{{Cite book |last=Peacock |first=J. A. |url=https://www.cambridge.org/core/product/identifier/9780511804533/type/book |title=Cosmological Physics |date=1998-12-28 |publisher=Cambridge University Press |isbn=978-0-521-41072-4 |edition=1 |doi=10.1017/cbo9780511804533}}</ref>{{rp|72}}

<math display="block">1+z = \frac{a_\mathrm{now}}{a_\mathrm{then}} = \frac{a_0}{a(t)}</math>

The scale factor is [[monotonic function|monotonically increasing]] as time passes. Thus {{math|''z''}} is positive, close to zero for local stars, and increasing for distant galaxies that appear redshifted.

Using a [[Friedmann–Robertson–Walker model]] of the expansion of the universe, redshift can be related to the age of an observed object, the so-called ''[[cosmic time]]–redshift relation''. Denote a density ratio as {{math|Ω<sub>0</sub>}}:

<math display="block">\Omega_0 = \frac {\rho}{ \rho_\text{crit}} \ , </math>

with {{math|''ρ''<sub>crit</sub>}} the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space.<ref Name=Weinberg>{{cite book |first=Steven | last=Weinberg |edition=2nd |title=The First Three Minutes: A Modern View of the Origin of the Universe | page=34 |isbn=9780-465-02437-7 |date=1993 |publisher=Basic Books|title-link=The First Three Minutes: A Modern View of the Origin of the Universe }}</ref> At large redshifts, {{math| ''1 + z'' > Ω<sub>0</sub><sup>−1</sup>}}, one finds:

<math display="block"> t(z) \approx \frac {2}{3 H_0 {\Omega_0}^{1/2} } z^{-3/2}\ , </math>

where {{math|''H''<sub>0</sub>}} is the present-day [[Hubble constant]], and {{math|''z''}} is the redshift.<ref name="Bergström">{{cite book |title=Cosmology and Particle Astrophysics |url=https://books.google.com/books?id=CQYu_sutWAoC&pg=PA77 |at=p. 77, Eq. 4.79 |isbn=978-3-540-32924-4 |publisher=Springer |edition=2nd|date=2006|first1 = Lars |last1=Bergström|first2 = Ariel |last2=Goobar|author-link1=Lars Bergström (physicist) |author-link2=Ariel Goobar }}</ref><ref name = Longair>{{cite book |title=Galaxy Formation |first=M. S. |last=Longair |url=https://books.google.com/books?id=2ARuLT-tk5EC&pg=PA161 |page=161 |isbn=978-3-540-63785-1 |publisher=Springer |date=1998}}</ref>

The '''cosmological redshift''' is commonly attributed to stretching of the wavelengths of photons due to the stretching of space. This interpretation can be misleading. 
As required by [[general relativity]], the cosmological expansion of space has no effect on local physics. There is no term related to expansion in [[Maxwell's equations]] that govern light propagation. The cosmological redshift can be interpreted as an accumulation of infinitesimal Doppler shifts along the trajectory of the light.<ref name="Hogg">{{cite journal |author=Bunn |first1=E. F. |last2=Hogg |first2=D. W. |year=2009 |title=The kinematic origin of the cosmological redshift |journal=American Journal of Physics |volume=77 |issue=8 |pages=688–694 |arxiv=0808.1081 |bibcode=2009AmJPh..77..688B |doi=10.1119/1.3129103 |s2cid=1365918}}</ref>

There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.<ref name="UCLA-2018">{{cite web |last=Wright |first=Edward L. |title=UCLA Cosmological Calculator |url=http://www.astro.ucla.edu/~wright/ACC.html |date=2018 |work=[[UCLA]] |access-date=6 August 2022 }} For parameter values as of 2018, H<sub>0</sub>=67.4 and Omega<sub>M</sub>=0.315; see the table at {{section link|Lambda-CDM model#Parameters}}.</ref><ref name="ICRAR-2022">{{cite web |title=ICRAR Cosmology Calculator |url=https://cosmocalc.icrar.org/ |date=2022 |work=[[International Centre for Radio Astronomy Research]] |access-date=6 August 2022 }}</ref>

====Distinguishing between cosmological and local effects====

The redshift of a galaxy includes both a component related to [[recessional velocity]] from expansion of the universe, and a component related to the [[peculiar motion]] of the galaxy with respect to its local universe.<ref>{{cite journal
 | title=A comparison between the Doppler and cosmological redshifts
 | last=Bedran | first=M. L. | year=2002
 | journal=American Journal of Physics
 | volume=70 | issue=4 | pages=406–408
 | doi=10.1119/1.1446856 | bibcode=2002AmJPh..70..406B
 | url=http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf
 | access-date=2023-03-16
}}</ref> The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity.<ref name="Harrison2">{{cite journal |last=Harrison |first=Edward |date=1992 |title=The redshift-distance and velocity-distance laws |journal=Astrophysical Journal |volume=403 |pages=28–31 |bibcode=1993ApJ...403...28H |doi=10.1086/172179 |doi-access=free }}</ref> Describing the cosmological expansion origin of redshift, cosmologist [[Edward Robert Harrison]] said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..."<ref>{{Harvnb|Harrison|2000|p=302}}.</ref> [[Steven Weinberg]] clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of {{math|''a''(''t'')}} [the [[Scale factor (cosmology)|scale factor]]] at the times of emission or absorption, but on the increase of {{math|''a''(''t'')}} in the whole period from emission to absorption."<ref name=Weinberg_Cosmology>{{cite book |url=https://books.google.com/books?id=48C-ym2EmZkC&pg=PA11 |first=Steven | last=Weinberg |title=Cosmology |publisher=Oxford University Press |page=11 |date=2008 |isbn=978-0-19-852682-7}}</ref>

===Gravitational redshift===
{{Main|Gravitational redshift}}
In the theory of [[general relativity]], there is time dilation within a gravitational well. Light emitted within the well will appear to have fewer cycles per second when measured outside of the well, due to differences in the two clocks.<ref>{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1st |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|284}}  This is known as the [[gravitational redshift]] or ''Einstein shift''.<ref>{{cite journal | last=Chant | first=C. A. | bibcode = 1930JRASC..24..390C | title = Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines) | date = 1930 | journal = [[Journal of the Royal Astronomical Society of Canada]] | volume = 24 | page = 390 }}</ref> The theoretical derivation of this effect follows from the [[Schwarzschild solution]] of the [[Einstein field equations|Einstein equations]] which yields the following formula for redshift associated with a photon travelling in the [[gravitational field]] of an [[Electric charge|uncharged]], [[rotation|nonrotating]], [[spherical symmetry|spherically symmetric]] mass:

<math display="block">1+z=\frac{1}{\sqrt{1-\frac{2GM}{rc^2}}},</math>

where
* {{math|''G''}} is the [[gravitational constant]],
* {{math|''M''}} is the [[mass]] of the object creating the gravitational field,
* {{math|''r''}} is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a [[Schwarzschild coordinates|Schwarzschild coordinate]]), and
* {{math|''c''}} is the [[speed of light]].

This gravitational redshift result can be derived from the assumptions of [[special relativity]] and the [[equivalence principle]]; the full theory of general relativity is not required.<ref>{{cite journal | last = Einstein | first = A. | author-link = Albert Einstein | date = 1907 | title = Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen |language=de |trans-title=On the relativity principle and the consequences drawn from it | journal = Jahrbuch der Radioaktivität und Elektronik | volume = 4 | bibcode=1908JRE.....4..411E |page=458 }}</ref>

The effect is very small but measurable on Earth using the [[Mössbauer effect]] and was first observed in the [[Pound–Rebka experiment]].<ref>{{cite journal | doi = 10.1103/PhysRevLett.4.337 | title = Apparent Weight of Photons | date = 1960 | last1 = Pound | first1 = R. | last2 = Rebka | first2 = G. | journal = Physical Review Letters | volume = 4 | issue = 7 | pages = 337–341 | bibcode=1960PhRvL...4..337P| doi-access = free }} This paper was the first measurement.</ref> However, it is significant near a [[black hole]], and as an object approaches the [[event horizon]] the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the [[cosmic microwave background]] radiation (see [[Sachs–Wolfe effect]]).<ref>{{cite journal | last1=Sachs | first1=R. K. | author-link=Rainer K. Sachs | last2=Wolfe | first2=A. M. | author-link2=Arthur M. Wolfe | date=1967 | title=Perturbations of a cosmological model and angular variations of the cosmic microwave background | journal=Astrophysical Journal | volume=147 | issue=73 | doi=10.1086/148982 | page=73 | bibcode=1967ApJ...147...73S }}</ref>

=== Summary table ===
Several important special-case formulae for redshift in certain special spacetime geometries are summarised in the following table. In all cases the magnitude of the shift (the value of {{math|''z''}}) is independent of the wavelength.{{refn|name="basicastronomy"|See {{harvnb|Binney| Merrifeld|1998}}, {{harvnb|Carroll|Ostlie|1996}}, {{harvnb|Kutner|2003}} for applications in astronomy.}}

{| class="wikitable" style="max-width:1000px;"
|+ Redshift summary
! Redshift type !! Geometry !! Formulae{{efn|text=Where {{mvar|z}} = redshift; {{mvar|v<sub><nowiki>||</nowiki></sub>}} = [[velocity]] parallel to line-of-sight (positive if moving away from receiver); {{mvar|c}} = [[speed of light]]; {{mvar|γ}} = [[Lorentz factor]]; {{mvar|a}} = [[scale factor (Universe)|scale factor]]; {{mvar|G}} = [[gravitational constant]]; {{mvar|M}} = object [[mass]]; {{mvar|r}} = [[Schwarzschild coordinates|radial Schwarzschild coordinate]], {{mvar|g<sub>tt</sub>}} = {{mvar|t,t}} component of the [[metric tensor]]}}
|-
| [[Relativistic Doppler effect|Relativistic Doppler]]|| [[Minkowski space]]<br />(flat spacetime) ||
For motion completely in the radial or<br />line-of-sight direction:

<math>1 + z = \gamma \left(1 + \frac{v_{\parallel}}{c}\right) = \sqrt{\frac{1+\frac{v_{\parallel}}{c}}{1-\frac{v_{\parallel}}{c}}}</math>

<math>z \approx \frac{v_{\parallel}}{c}</math> for&nbsp;small <math>v_{\parallel}</math>

For motion completely in the transverse direction:

<math display="block">1 + z=\frac{1}{\sqrt{1-\frac{v_\perp^2}{c^2}}}</math>

<math>z \approx \frac{1}{2} \left( \frac{v_{\perp}}{c} \right)^2</math>
for&nbsp;small <math>v_{\perp}</math>

|-
| [[Cosmological redshift]]|| [[Friedmann–Lemaître–Robertson–Walker metric|FLRW spacetime]]<br />(expanding Big Bang universe) || 
<math display="block">1 + z = \frac{a_{\mathrm{now}}}{a_{\mathrm{then}}}</math>

[[Hubble's law]]:

<math display="block">z \approx \frac{H_0 D}{c}</math>
for <math>D \ll \frac{c}{H_0}</math>

|-
| [[Gravitational redshift]]|| Any [[stationary spacetime]] || 
<math display="block">1 + z = \sqrt{\frac{g_{tt}(\text{receiver})}{g_{tt}(\text{source})}}</math>

For the [[Schwarzschild geometry]]:

<math display="block">1 + z = \sqrt{\frac{1 - \frac{r_S}{r_{\text{receiver}}}}{1 - \frac{r_S}{r_{\text{source} }}}} = \sqrt{\frac{1 - \frac{2GM}{ c^2  r_{\text{receiver}}}}{1 - \frac{2GM}{ c^2 r_{\text{source} }}}} </math>

<math>z \approx \frac{1}{2} \left( \frac{r_S}{r_\text{source}} - \frac{r_S}{r_\text{receiver}} \right)</math> for <math>r \gg r_S</math>

In terms of [[escape velocity]]:

<math>z \approx \frac{1}{2} \left(\frac{v_\text{e}}{c}\right)_\text{source}^2 - \frac{1}{2} \left(\frac{v_\text{e}}{c}\right)_\text{receiver}^2 </math> 
for <math>v_\text{e} \ll c</math>

|}
{{notelist}}

==Observations in astronomy==
[[File:Look-back time by redshift.png|thumb|The [[lookback time]] by observed redshift up to {{nowrap|1={{mvar|z}} = 20}} using parameters of the [[Planck mission]] in the [[Lambda CDM|standard model of cosmology]].<ref name="Pilipenko">{{cite arXiv |eprint=1303.5961 |last1=Pilipenko |first1=Sergey V. |title=Paper-and-pencil cosmological calculator |date=2013 |class=astro-ph.CO}} Includes algorithm used to draw the graph.</ref> There are websites for calculating distances from redshift.<ref name="UCLA-2018"/><ref name="ICRAR-2022"/>]]

The redshift observed in astronomy can be measured because the [[emission spectrum|emission]] and [[Absorption spectroscopy|absorption]] spectra for [[atom]]s are distinctive and well known, calibrated from [[spectroscopic]] experiments in [[laboratories]] on Earth. When the redshifts of various absorption and emission lines from a single astronomical object are measured, {{math|''z''}} is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by [[Kinetic theory of gases|thermal]] or mechanical [[motion]] of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts.

Spectroscopy, as a measurement, is considerably more difficult than simple [[photometry (astronomy)|photometry]], which measures the [[brightness]] of astronomical objects through certain [[Optical filter|filters]].<!--General source on photometry is not needed. That's what the article on the subject is for--> When photometric data is all that is available (for example, the [[Hubble Deep Field]] and the [[Hubble Ultra Deep Field]]), astronomers rely on a technique for measuring [[photometric redshift]]s.<ref>The technique was first described by: {{cite conference | last=Baum | first=W. A. | year=1962 | editor-first=G. C. | editor-last=McVittie | title=Problems of extra-galactic research | page=390 | conference=IAU Symposium No. 15 }}</ref> Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, [[observational error|errors]] for these sorts of measurements can range up to {{math|δ''z'' {{=}} 0.5}}, and are much less reliable than spectroscopic determinations.<ref>{{cite journal | last1=Bolzonella | first1=M. | last2=Miralles | first2=J.-M. | last3=Pelló | first3=R. | title=Photometric redshifts based on standard SED fitting procedures | journal=Astronomy and Astrophysics | volume=363 | pages=476–492 | year=2000 | arxiv=astro-ph/0003380 | bibcode=2000A&A...363..476B }}</ref>

However, photometry does at least allow a qualitative characterisation of a redshift. For example, if a Sun-like spectrum had a redshift of {{math|''z'' {{=}} 1}}, it would be brightest in the [[infrared]] (1000&nbsp;nm) rather than at the blue-green (500&nbsp;nm) color associated with the peak of its [[Black body|blackbody]] spectrum, and the light intensity will be reduced in the filter by a factor of four, {{math|(1 + ''z''){{sup|2}}}}. Both the photon count rate and the photon energy are redshifted. (See [[K correction]] for more details on the photometric consequences of redshift.)<!--General source on K correction is not needed. That's what the article on the subject is for-->

Determining the redshift of an object with spectroscopy requires the wavelength of the emitted light in the rest frame of the source. Astronomical applications rely on distinct spectral lines. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or [[white noise]] (random fluctuations in a spectrum). Thus [[gamma-ray burst]]s themselves cannot be used for reliable redshift measurements, but optical afterglow associated with the burst can be analysed for redshifts.<ref>{{Cite web |title=Swift: About Swift |url=https://swift.gsfc.nasa.gov/about_swift/redshift.html |access-date=2025-04-07 |website=swift.gsfc.nasa.gov}}</ref>

===Local observations===
In nearby objects (within our [[Milky Way]] galaxy) observed redshifts are almost always related to the [[Line-of-sight propagation|line-of-sight]] velocities associated with the objects being observed. Observations of such redshifts and blueshifts enable astronomers to measure [[velocity|velocities]] and parametrise the [[mass]]es of the [[orbit]]ing [[star]]s in [[spectroscopic binaries]]. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to [[Methods of detecting exoplanets#Radial velocity|diagnose and measure]] the presence and characteristics of [[Exoplanet|planetary systems]] around other stars and have even made very [[Rossiter–McLaughlin effect|detailed differential measurements]] of redshifts during [[Methods of detecting exoplanets|planetary transits]] to determine precise orbital parameters. Some approaches are able to track the redshift variations in multiple objects at once.<ref>{{cite journal |last1=Ge |first1=Jian |last2=Van Eyken |first2=Julian |last3=Mahadevan |first3=Suvrath |author3-link=Suvrath Mahadevan |last4=Dewitt |first4=Curtis |last5=Kane |first5=Stephen R. |last6=Cohen |first6=Roger |last7=Vanden Heuvel |first7=Andrew |last8=Fleming |first8=Scott W. |last9=Guo |first9=Pengcheng |last10=Henry |first10=Gregory W. |last11=Schneider |first11=Donald P. |last12=Ramsey |first12=Lawrence W. |last13=Wittenmyer |first13=Robert A. |last14=Endl |first14=Michael |last15=Cochran |first15=William D. |display-authors=4 |date=2006 |title=The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument |journal=The Astrophysical Journal |volume=648 |issue=1 |pages=683–695 |arxiv=astro-ph/0605247 |bibcode=2006ApJ...648..683G |doi=10.1086/505699 |s2cid=13879217 |last16=Ford |first16=Eric B. |last17=Martin |first17=Eduardo L. |last18=Israelian |first18=Garik |last19=Valenti |first19=Jeff |last20=Montes |first20=David}}</ref>

Finely detailed measurements of redshifts are used in [[helioseismology]] to determine the precise movements of the [[photosphere]] of the [[Sun]].<ref>{{cite journal | doi = 10.1007/BF00243557 | title = Solar and stellar seismology | date = 1988 | last1 = Libbrecht | first1 = Keng | journal = Space Science Reviews | volume = 47 | issue = 3–4 |bibcode=1988SSRv...47..275L | pages=275–301| s2cid = 120897051 | url = https://authors.library.caltech.edu/104214/1/1988SSRv___47__275L.pdf }}</ref> Redshifts have also been used to make the first measurements of the [[rotation]] rates of [[planet]]s,<ref>{{Cite journal |last1=Gaulme |first1=Patrick |last2=Schmider |first2=François-Xavier |last3=Gonçalves |first3=Ivan |date=2018-09-01 |title=Measuring planetary atmospheric dynamics with Doppler spectroscopy |url=https://www.aanda.org/articles/aa/abs/2018/09/aa32868-18/aa32868-18.html |journal=Astronomy & Astrophysics |language=en |volume=617 |pages=A41 |doi=10.1051/0004-6361/201832868 |issn=0004-6361|arxiv=1804.09445 |bibcode=2018A&A...617A..41G }}</ref> velocities of [[interstellar cloud]]s,<ref>An early review on the subject: {{cite journal | title=The formation of galaxies and the origin of the high-velocity hydrogen | journal=[[Astronomy and Astrophysics]] | volume=7 | page=381 | date=1970 | bibcode=1970A&A.....7..381O | last= Oort | first= J. H. |author-link=Jan Hendrik Oort}}</ref> the [[Galaxy rotation curve|rotation of galaxies]],<ref name="basicastronomy"/> and the [[dynamics (mechanics)|dynamics]] of [[Accretion disk|accretion]] onto [[neutron star]]s and [[black hole]]s which exhibit both Doppler and gravitational redshifts.<ref>{{cite journal| last=Asaoka | first=Ikuko | bibcode=1989PASJ...41..763A | title=X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole | journal=Publications of the Astronomical Society of Japan | volume=41 | issue=4 | date=1989 | pages=763–778 | doi=10.1093/pasj/41.4.763 }}</ref> The [[temperature]]s of various emitting and absorbing objects can be obtained by measuring [[Doppler broadening]]—effectively redshifts and blueshifts over a single emission or absorption line.<ref>{{cite book | last1=Rybicki | first1=G. B. | first2=A. R. | last2=Lightman | title=Radiative Processes in Astrophysics | publisher=John Wiley & Sons | year=1979 | page=288 | isbn=0-471-82759-2 }}</ref> By measuring the broadening and shifts of the 21-centimeter [[hydrogen line]] in different directions, astronomers have been able to measure the [[Recessional velocity|recessional velocities]] of [[interstellar gas]], which in turn reveals the [[rotation curve]] of our Milky Way.<ref name="basicastronomy"/> Similar measurements have been performed on other galaxies, such as [[Andromeda Galaxy|Andromeda]].<ref name="basicastronomy"/>

===Extragalactic observations===

The most distant objects exhibit larger redshifts corresponding to the [[Hubble flow]] of the [[universe]]. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the [[cosmic microwave background]] radiation; the [[Hubble's law#Redshift velocity|numerical value of its redshift]] is about {{math|''z'' {{=}} 1089}} ({{math|''z'' {{=}} 0}} corresponds to present time), and it shows the state of the universe about 13.8 billion years ago,<ref>{{cite web
 | title=Cosmic Detectives
 | url=http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives
 | publisher=The European Space Agency (ESA)
 | date=2013-04-02
 | access-date=2013-04-25
}}</ref> and 379,000 years after the initial moments of the [[Big Bang]].

The luminous point-like cores of [[quasar]]s were the first "high-redshift" ({{math|''z'' > 0.1}}) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.<ref name="Kellermann">{{cite journal |last1=Kellermann |first1=K. I. |title=The Discovery of Quasars and its Aftermath |journal=Journal of Astronomical History and Heritage |date=2014 |volume=17 |issue=3 |pages=267–282 |doi=10.3724/SP.J.1440-2807.2014.03.03 |arxiv=1304.3627 }}</ref>

For galaxies more distant than the [[Local Group]] and the nearby [[Virgo Cluster]], but within a thousand mega[[parsec]]s or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by [[Edwin Hubble]] and has come to be known as [[Hubble's law]]. [[Vesto Slipher]] was the first to discover galactic redshifts, in about 1912, while Hubble correlated Slipher's measurements with distances he [[cosmic distance ladder|measured by other means]] to formulate his law.{{sfn|Peebles|1993|pp=78–79}} Because it is usually not known how [[luminosity|luminous]] objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.<ref>{{Cite web |last=Halstead |first=Evan |date=2021-08-16 |title=Introduction to General Relativity: 7.3: Redshift |url=https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/07:_Cosmology/7.03:_Redshift |access-date=2025-03-06 |website=Physics LibreTexts |language=en}}</ref>

[[Gravitation]]al interactions of galaxies with each other and clusters cause a significant [[variance|scatter]] in the normal plot of the Hubble diagram. The [[peculiar velocity|peculiar velocities]] associated with galaxies superimpose a rough trace of the [[mass]] of [[virial theorem|virialised objects]] in the universe. This effect leads to such phenomena as nearby galaxies (such as the [[Andromeda Galaxy]]) exhibiting blueshifts as we fall towards a common [[barycenter]], and redshift maps of clusters showing a [[fingers of god]] effect due to the scatter of peculiar velocities in a roughly spherical distribution.{{sfn|Peebles|1993|p=34}} These "redshift-space distortions" can be used as a cosmological probe in their own right, providing information on how structure formed in the universe,<ref>{{cite journal|last1=Percival|first1=Will J.|last2=White|first2=Martin|title=Testing cosmological structure formation using redshift-space distortions|journal=Monthly Notices of the Royal Astronomical Society|date=11 February 2009|volume=393|issue=1|pages=297–308|doi=10.1111/j.1365-2966.2008.14211.x|doi-access=free |arxiv = 0808.0003 |bibcode = 2009MNRAS.393..297P }}</ref> and how gravity behaves on large scales.<ref>{{cite journal|last1=Raccanelli|first1=A.|last2=Bertacca|first2=D.|last3=Pietrobon|first3=D.|last4=Schmidt|first4=F.|last5=Samushia|first5=L.|last6=Bartolo|first6=N.|last7=Dore|first7=O.|last8=Matarrese|first8=S.|last9=Percival|first9=W. J.|title=Testing gravity using large-scale redshift-space distortions|journal=Monthly Notices of the Royal Astronomical Society|date=25 September 2013|volume=436|issue=1|pages=89–100|doi=10.1093/mnras/stt1517|doi-access=free |arxiv = 1207.0500 |bibcode = 2013MNRAS.436...89R }}</ref>

The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.<ref>{{Cite web |last=Knox |first=Lloyd |date=2016-12-22 |title=Physics 156: A Cosmology Workbook: 1.7: The Distance-Redshift Relation |url=https://phys.libretexts.org/Courses/University_of_California_Davis/Physics_156:_A_Cosmology_Workbook/01:_Workbook/1.07:_The_Distance-Redshift_Relation |access-date=2025-03-06 |website=Physics LibreTexts |language=en}}</ref>

It was long believed that the expansion rate has been continuously decreasing since the Big Bang, but observations beginning in 1988 of the redshift-distance relationship using [[Type Ia supernova]]e have suggested that in comparatively recent times the expansion rate of the universe has [[Accelerating expansion of the universe|begun to accelerate]].<ref>{{cite web|url=https://www.nobelprize.org/uploads/2019/05/popular-physicsprize2011.pdf |title=The Nobel Prize in Physics 2011: Information for the Public |publisher=Nobel Foundation |access-date=2023-06-13}}</ref>

===Highest redshifts===
{{see also|List of the most distant astronomical objects#List of most distant objects by type{{!}}List of most distant astronomical objects by type}}
[[File:Comoving distance and lookback time (Planck 2018).png|thumb|upright=1.8|[[Comoving and proper distances|Comoving distance]] and [[lookback time]] for the Planck 2018 cosmology parameters, from redshift 0 to 15, with distance (blue solid line) on the left axis, and time (orange dashed line) on the right. Note that the time that has passed (in billions of years) from a given redshift until now is not the same as the distance (in giga light years) light would have travelled from that redshift, due to the expansion of the universe over the intervening period.]]

The most reliable redshifts are from [[spectroscopic]] data,<ref>{{Cite web |title=Redshift |url=https://lco.global/spacebook/light/redshift/ |access-date=2025-03-06 |publisher=[[Las Cumbres Observatory]] |language=en}}</ref> and the highest-confirmed spectroscopic redshift of a galaxy is that of [[JADES-GS-z14-0]] with a redshift of {{math|''z'' {{=}} 14.32}}, corresponding to 290 million years after the Big Bang.<ref>{{Cite journal |last1=Carniani |first1=Stefano |last2=Hainline |first2=Kevin |last3=D'Eugenio |first3=Francesco |last4=Eisenstein |first4=Daniel J. |last5=Jakobsen |first5=Peter |last6=Witstok |first6=Joris |last7=Johnson |first7=Benjamin D. |last8=Chevallard |first8=Jacopo |last9=Maiolino |first9=Roberto |last10=Helton |first10=Jakob M. |last11=Willott |first11=Chris |last12=Robertson |first12=Brant |last13=Alberts |first13=Stacey |last14=Arribas |first14=Santiago |last15=Baker |first15=William M. |display-authors=6 |date=2024-07-29 |title=Spectroscopic confirmation of two luminous galaxies at a redshift of 14 |journal=Nature |volume=633 |issue=8029 |language=en |pages=318–322 |doi=10.1038/s41586-024-07860-9 |issn=1476-4687|doi-access=free |pmid=39074505 |pmc=11390484 |arxiv=2405.18485 |bibcode=2024Natur.633..318C }}</ref> The previous record was held by [[GN-z11]],<ref>{{cite journal
 | title=A Remarkably Luminous Galaxy at z=11.1 Measured with Hubble Space Telescope Grism Spectroscopy
 | last1=Oesch | first1=P. A. | last2=Brammer | first2=G.
 | last3=van Dokkum | first3=P. G. | last4=Illingworth | first4=G. D.
 | last5=Bouwens | first5=R. J. | last6=Labbé | first6=I.
 | last7=Franx | first7=M. | last8=Momcheva | first8=I.
 | last9=Ashby | first9=M. L. N. | last10=Fazio | first10=G. G.
 | last11=Gonzalez | first11=V. | last12=Holden | first12=B.
 | last13=Magee | first13=D. | last14=Skelton | first14=R. E.
 | last15=Smit | first15=R. | last16=Spitler | first16=L. R.
 | last17=Trenti | first17=M. | last18=Willner | first18=S. P.
 | display-authors=6 | journal=The Astrophysical Journal
 | date=March 1, 2016 | volume=819 | issue=2 | page=129
 | arxiv=1603.00461 | doi=10.3847/0004-637X/819/2/129
 | bibcode=2016ApJ...819..129O | s2cid=119262750
| doi-access=free }}</ref> with a redshift of {{math|''z'' {{=}} 11.1}}, corresponding to 400 million years after the Big Bang.

Slightly less reliable are [[Lyman-break galaxy|Lyman-break]] redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift {{math|''z'' {{=}} 7.5}}<ref>{{Cite journal|last1=Watson|first1=Darach|last2=Christensen|first2=Lise|last3=Knudsen|first3=Kirsten Kraiberg|last4=Richard|first4=Johan|last5=Gallazzi|first5=Anna|last6=Michałowski|first6=Michał Jerzy|title=A dusty, normal galaxy in the epoch of reionization|journal=Nature|volume=519|issue=7543|pages=327–330|doi=10.1038/nature14164|arxiv = 1503.00002 |bibcode = 2015Natur.519..327W|pmid=25731171|year=2015|s2cid=2514879}}</ref><ref>{{cite journal
 | title=Discovery of a Very Bright Strongly Lensed Galaxy Candidate at z ~ 7.6
 | first1=L. D. | last1=Bradley | first2=R. J. | last2=Bouwens
 | first3=H. C. | last3=Ford | first4=G. D. | last4=Illingworth
 | first5=M. J. | last5=Jee | first6=N. | last6=Benítez
 | first7=T. J. | last7=Broadhurst | first8=M. | last8=Franx
 | first9=B. L. | last9=Frye | first10=L. | last10=Infante
 | display-authors=6 | journal=[[The Astrophysical Journal]]
 | volume=678 | issue=2 | pages=647–654 | year=2008
 | bibcode=2008ApJ...678..647B | s2cid=15574239
 | doi=10.1086/533519 | arxiv=0802.2506
}}</ref> and the next highest being {{math|''z'' {{=}} 7.0}}.<ref>{{cite journal
 | display-authors=6 | first1=E. | last1=Egami
 | first2=J.-P. | last2=Kneib | first3=G. H. | last3=Rieke
 | first4=R. S. | last4=Ellis | first5=J. | last5=Richard
 | first6=J. | last6=Rigby | first7=C. | last7=Papovich
 | first8=D. | last8=Stark | first9=M. R. | last9=Santos
 | first10=J.-S. | last10=Huang | first11=H. | last11=Dole
 | first12=E. Le | last12=Floc'H | first13=P. G. | last13=Pérez-González
 | title=Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218
 | journal=[[The Astrophysical Journal]]
 | volume=618 | issue=1 | pages=L5–L8 | year=2005
 | bibcode=2005ApJ...618L...5E | doi=10.1086/427550
 | arxiv=astro-ph/0411117 | s2cid=15920310 }}</ref> The most distant-observed [[gamma-ray burst]] with a spectroscopic redshift measurement was [[GRB 090423]], which had a redshift of {{math|''z'' {{=}} 8.2}}.<ref>{{cite journal
 | title=GRB 090423 reveals an exploding star at the epoch of re-ionization
 | last1=Salvaterra | first1=R. | first2=M. Della | last2=Valle
 | last3=Campana | first3=S. |author-link3=Sergio Campana (astrophysicist)| last4=Chincarini | first4=G.
 | last5=Covino | first5=S. | last6=d'Avanzo | first6=P.
 | last7=Fernández-Soto | first7=A. | last8=Guidorzi | first8=C.
 | last9=Mannucci | first9=F. | last10=Margutti | first10=R.
 | last11=Thöne | first11=C. C. | last12=Antonelli | first12=L. A.
 | last13=Barthelmy | first13=S. D. | last14=De Pasquale | first14=M.
 | last15=d'Elia | first15=V. | last16=Fiore | first16=F.
 | last17=Fugazza | first17=D. | last18=Hunt | first18=L. K.
 | last19=Maiorano | first19=E. | last20=Marinoni | first20=S.
 | last21=Marshall | first21=F. E. | last22=Molinari | first22=E.
 | last23=Nousek | first23=J. | last24=Pian | first24=E.
 | last25=Racusin | first25=J. L. | last26=Stella | first26=L.
 | last27=Amati | first27=L. | last28=Andreuzzi | first28=G.
 | last29=Cusumano | first29=G. | last30=Fenimore | first30=E. E.
 | display-authors=4 | journal=[[Nature (journal)|Nature]]
 | volume=461 | issue=7268 | pages=1258–60
 | doi=10.1038/nature08445 | date=2009 | pmid=19865166
 | s2cid=205218263 | bibcode=2009Natur.461.1258S |arxiv=0906.1578
 }}</ref> The most distant-known quasar, [[ULAS J1342+0928]], is at {{math|''z'' {{=}} 7.54}}.<ref>{{cite web|url=https://news.mit.edu/2017/scientists-observe-supermassive-black-hole-infant-universe-1206|title=Scientists observe supermassive black hole in infant universe|website=MIT News |publisher=Massachusetts Institute of Technology |date=2017-12-06 |first=Jennifer |last=Chu}}</ref><ref name="Nature-2018-01">{{cite journal |last1=Bañados |first1=Eduardo |last2=Venemans |first2=Bram P. |last3=Mazzucchelli |first3=Chiara |last4=Farina |first4=Emanuele P. |last5=Walter |first5=Fabian |last6=Wang |first6=Feige |last7=Decarli |first7=Roberto |last8=Stern |first8=Daniel |last9=Fan |first9=Xiaohui |last10=Davies |first10=Frederick B. |last11=Hennawi |first11=Joseph F. |last12=Simcoe |first12=Robert A. |last13=Turner |first13=Monica L. |last14=Rix |first14=Hans-Walter |last15=Yang |first15=Jinyi |last16=Kelson |first16=Daniel D. |last17=Rudie |first17=Gwen C. |last18=Winters |first18=Jan Martin |display-authors=6  |title=An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5 |journal=Nature |date=January 2018 |volume=553 |issue=7689 |pages=473–476 |doi=10.1038/nature25180 |pmid=29211709 |arxiv=1712.01860 |bibcode=2018Natur.553..473B |s2cid=205263326 }}</ref> The highest-known redshift radio galaxy (TGSS1530) is at a redshift {{math|''z'' {{=}} 5.72}}<ref>{{cite journal|last1=Saxena|first1=A.|date=2018|title=Discovery of a radio galaxy at z = 5.72|journal=Monthly Notices of the Royal Astronomical Society|volume=480|issue=2|pages=2733–2742|arxiv=1806.01191|bibcode=2018MNRAS.480.2733S|doi=10.1093/mnras/sty1996|doi-access=free |s2cid=118830412}}</ref> and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at {{math|''z'' {{=}} 6.42}}.<ref>{{cite journal | doi = 10.1038/nature01821 | title = Molecular gas in the host galaxy of a quasar at redshift z = 6.42 | date = 2003 | last1 = Walter | first1 = Fabian | last2 = Bertoldi | first2 = Frank | last3 = Carilli | first3 = Chris | last4 = Cox | first4 = Pierre | last5 = Lo | first5 = K. Y. | last6 = Neri | first6 = Roberto | last7 = Fan | first7 = Xiaohui | last8 = Omont | first8 = Alain | last9 = Strauss | first9 = Michael A. | last10 = Menten | first10 = Karl M. |display-authors=6 | journal = Nature | volume = 424 | issue = 6947 | pages = 406–408 | pmid = 12879063 |bibcode=2003Natur.424..406W|arxiv = astro-ph/0307410 |s2cid = 4419009 }}</ref>

''Extremely red objects'' (EROs) are [[Radio astronomy#Astronomical sources|astronomical sources]] of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.<ref>
{{cite journal
 | display-authors=4
 | last1=Smail |first1=Ian
 | last2=Owen |first2=F. N.
 | last3=Morrison |first3=G. E.
 | last4=Keel |first4=W. C.
 | last5=Ivison |first5=R. J.
 | last6=Ledlow |first6=M. J.
 | journal=The Astrophysical Journal | volume=581 | issue=2
 | pages=844–864 | doi=10.1086/344440 | bibcode=2002ApJ...581..844S
 | title=The Diversity of Extremely Red Objects
 | date=2002
|arxiv = astro-ph/0208434 | s2cid=51737034
 }}</ref> Objects that are even redder than EROs are termed ''hyper extremely red objects'' (HEROs).<ref>
{{cite journal
 | last1=Totani |first1=Tomonori
 | last2=Yoshii |first2=Yuzuru
 | last3=Iwamuro |first3=Fumihide
 | last4=Maihara |first4=Toshinori
 | last5=Motohara |first5=Kentaro
 | title=Hyper Extremely Red Objects in the Subaru Deep Field: Evidence for Primordial Elliptical Galaxies in the Dusty Starburst Phase
 | journal=The Astrophysical Journal | volume=558 | issue=2
 | date=2001 | pages=L87–L91 | doi=10.1086/323619
 | bibcode=2001ApJ...558L..87T
|arxiv = astro-ph/0108145 | s2cid=119511017
 }}</ref>

The [[cosmic microwave background]] has a redshift of {{math|z {{=}} 1089}}, corresponding to an age of approximately 379,000 years after the Big Bang and a [[Comoving and proper distances|proper distance]] of more than 46 billion light-years.<ref name="ly93">
{{cite journal | last1 = Lineweaver | first1 = Charles | first2=Tamara M. | last2=Davis | date = 2005 | title = Misconceptions about the Big Bang | journal = Scientific American | volume = 292 | issue = 3 | pages = 36–45 | doi = 10.1038/scientificamerican0305-36 | bibcode = 2005SciAm.292c..36L }}</ref> This redshift corresponds to a shift in average temperature from 3000&nbsp;K down to 3&nbsp;K.<ref>{{cite journal|last1=Gawiser|first1=E.|last2=Silk|first2=J.|date=2000|title=The cosmic microwave background radiation|journal=[[Physics Reports]]|volume=333–334|issue=2000|pages=245–267|doi=10.1016/S0370-1573(00)00025-9|arxiv=astro-ph/0002044|bibcode = 2000PhR...333..245G |citeseerx=10.1.1.588.3349|s2cid=15398837}}</ref> The yet-to-be-observed first light from the oldest [[Population III stars]], not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of {{math|20 < ''z'' < 100}}.<ref>{{cite journal|bibcode=2006MNRAS.373L..98N|arxiv = astro-ph/0604050 |doi = 10.1111/j.1745-3933.2006.00251.x|title=The first stars in the Universe|date=2006|last1=Naoz|first1=S.|last2=Noter|first2=S.|last3=Barkana|first3=R.|journal=Monthly Notices of the Royal Astronomical Society: Letters|volume=373|issue = 1 |pages=L98–L102 |doi-access = free |s2cid = 14454275 }}</ref> Other high-redshift events predicted by physics but not presently observable are the [[cosmic neutrino background]] from about two seconds after the Big Bang (and a redshift in excess of {{math|''z'' > 10{{sup|10}}}})<ref>{{cite journal|bibcode=2006PhR...429..307L|arxiv = astro-ph/0603494 |doi = 10.1016/j.physrep.2006.04.001|title=Massive neutrinos and cosmology|date=2006|last1=Lesgourgues|first1=J.|last2=Pastor|first2=S.|journal=Physics Reports|volume=429|issue=6|pages=307–379 |s2cid = 5955312 }}</ref> and the cosmic [[gravitational wave background]] emitted directly from [[inflation (cosmology)|inflation]] at a redshift in excess of {{math|''z'' > 10{{sup|25}}}}.<ref>{{cite journal|bibcode=2005PhyU...48.1235G|arxiv = gr-qc/0504018 |doi = 10.1070/PU2005v048n12ABEH005795|title=Relic gravitational waves and cosmology|date=2005|last1=Grishchuk|first1=Leonid P.|journal=Physics-Uspekhi|volume=48|issue=12|pages=1235–1247 |s2cid = 11957123 }}</ref>

In June 2015, astronomers reported evidence for [[Stellar population#Population III stars|Population III stars]] in the [[Cosmos Redshift 7]] [[galaxy]] at {{math|''z'' {{=}} 6.60}}. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of [[chemical element]]s heavier than [[hydrogen]] that are needed for the later formation of [[planet]]s and [[life]] as we know it.<ref name="AJ-20150604">{{cite journal |last1=Sobral |first1=David |last2=Matthee |first2=Jorryt |last3=Darvish |first3=Behnam |last4=Schaerer |first4=Daniel |last5=Mobasher |first5=Bahram |last6=Röttgering |first6=Huub J. A. |last7=Santos |first7=Sérgio |last8=Hemmati |first8=Shoubaneh |title=Evidence For POPIII-Like Stellar Populations In The Most Luminous LYMAN-α Emitters At The Epoch Of Re-Ionisation: Spectroscopic Confirmation |date=4 June 2015 |journal=[[The Astrophysical Journal]] |doi=10.1088/0004-637x/808/2/139 |bibcode=2015ApJ...808..139S |volume=808 |issue=2 |page=139|arxiv=1504.01734|s2cid=18471887 }}</ref><ref name="NYT-20150617">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Astronomers Report Finding Earliest Stars That Enriched Cosmos |url=https://www.nytimes.com/2015/06/18/science/space/astronomers-report-finding-earliest-stars-that-enriched-cosmos.html |date=17 June 2015 |work=[[The New York Times]] |access-date=17 June 2015 }}</ref>

===Redshift surveys===
{{Main|Redshift survey}}
[[File:2dfgrs.png|thumb|Rendering of the 2dFGRS data]]
With advent of [[robotic telescope|automated telescopes]] and improvements in [[astronomical spectroscopy|spectroscopes]], a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the [[Observable universe|large-scale structure]] of the universe. The [[CfA2 Great Wall|Great Wall]], a vast [[supercluster]] of galaxies over 500 million [[light-year]]s wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.<ref>{{cite journal | title=Mapping the Universe | first1=M. J. | last1=Geller | first2=J. P. | last2=Huchra | journal=Science | volume=246 | issue=4932 | pages=897–903 | year=1989 | doi=10.1126/science.246.4932.897 | pmid=17812575 | bibcode=1989Sci...246..897G | s2cid=31328798 }}</ref>

The first redshift survey was the [[CfA Redshift Survey]], started in 1977 with the initial data collection completed in 1982.<ref>{{cite web
 | title=The CfA Redshift Survey
 | first=John P. | last=Huchra | author-link=John Huchra
 | publisher=Harvard & Smithsonian Center for Astrophysics
 | url=https://lweb.cfa.harvard.edu/~dfabricant/huchra/zcat/
 | access-date=2023-03-20
}}</ref> More recently, the [[2dF Galaxy Redshift Survey]] determined the large-scale structure of one section of the universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the final [[data set]] was released 30 June 2003.<ref>{{cite journal
 |title=The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications
 | first1=Shaun | last1=Cole | author-link=Shaun Cole
 | last2=Percival | first2=Will J. | last3=Peacock | first3=John A.
 | last4=Norberg | first4=Peder | last5=Baugh | first5=Carlton M.
 | last6=Frenk | first6=Carlos S. | last7=Baldry | first7=Ivan
 | last8=Bland-Hawthorn | first8=Joss | last9=Bridges | first9=Terry
 | last10=Cannon | first10=Russell | last11=Colless | first11=Matthew
 | last12=Collins | first12=Chris | last13=Couch | first13=Warrick
 | last14=Cross | first14=Nicholas J. G. | last15=Dalton | first15=Gavin
 | last16=Eke | first16=Vincent R. | last17=De Propris | first17=Roberto
 | last18=Driver | first18=Simon P. | last19=Efstathiou | first19=George
 | last20=Ellis | first20=Richard S. | last21=Glazebrook | first21=Karl
 | last22=Jackson | first22=Carole | last23=Jenkins | first23=Adrian
 | last24=Lahav | first24=Ofer | last25=Lewis | first25=Ian
 | last26=Lumsden | first26=Stuart | last27=Maddox | first27=Steve
 | last28=Madgwick | first28=Darren | last29=Peterson | first29=Bruce A.
 | last30=Sutherland | first30=Will | last31=Taylor | first31=Keith
 | display-authors=6
 | journal=Monthly Notices of the Royal Astronomical Society
 | volume=362 | issue=2 | pages=505–34 | date=2005
 | bibcode=2005MNRAS.362..505C | arxiv=astro-ph/0501174
 | doi=10.1111/j.1365-2966.2005.09318.x
 | doi-access=free | s2cid=6906627
}}</ref><ref>{{Cite web |title=2dF Galaxy Redshift Survey homepage |url=http://msowww.anu.edu.au:80/2dFGRS/ |archive-url=http://web.archive.org/web/20120322090959/http://msowww.anu.edu.au:80/2dFGRS/ |archive-date=2012-03-22 |access-date=2025-10-21 |website=msowww.anu.edu.au}}</ref> The [[Sloan Digital Sky Survey]] (SDSS) began collecting data in 1998<ref>{{cite journal |last1=Gunn |first1=James E. |last2=Siegmund |first2=Walter A. |last3=Mannery |first3=Edward J. |last4=Owen |first4=Russell E. |last5=Hull |first5=Charles L. |last6=Leger |first6=R. French |display-authors=etal |date=April 2006 |title=The 2.5 m Telescope of the Sloan Digital Sky Survey |journal=The Astronomical Journal |volume=131 |issue=4 |pages=2332–2359 |doi=10.1086/500975 |doi-access=free |arxiv=astro-ph/0602326 |bibcode=2006AJ....131.2332G }}</ref> and published its eighteenth data release in 2023.<ref>{{cite journal|last1=Almeida |first1=Andrés |display-authors=etal |title=The Eighteenth Data Release of the Sloan Digital Sky Surveys: Targeting and First Spectra from SDSS-V |journal=The Astrophysical Journal Supplement Series |date=2023 |volume=267 |number=2 |page=44 |doi=10.3847/1538-4365/acda98 |doi-access=free |arxiv=2301.07688 |bibcode=2023ApJS..267...44A}}</ref> SSDS has measured redshifts for galaxies as high as 0.8, and has recorded over 100,000 [[quasar]]s at {{math|''z'' {{=}} 3}} and beyond.<ref>{{cite web|url=https://www.sdss4.org/science/ |title=Science Results |website=SSDS |access-date=2025-05-20 }}</ref> The [[DEEP2 Redshift Survey]] used the [[Keck telescopes]] with the "DEIMOS" [[spectrograph]]; a follow-up to the pilot program DEEP1, DEEP2 was designed to measure faint galaxies with redshifts 0.7 and above, and it recorded redshifts of over 38,000 objects by its conclusion in 2013.<ref>{{cite conference | title=Science objectives and early results of the DEEP2 redshift survey| first1=Marc | last1=Davis |collaboration=DEEP2 collaboration |date=2002 | conference=Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 August 2002 | arxiv=astro-ph/0209419 | bibcode=2003SPIE.4834..161D | doi=10.1117/12.457897 }}</ref><ref>{{cite journal|first1=Jeffrey A. |last1=Newman |display-authors=etal |title=The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts |journal=The Astrophysical Journal Supplement Series |year=2013 |volume=208 |number=1 |page=5 |doi=10.1088/0067-0049/208/1/5|arxiv=1203.3192 |bibcode=2013ApJS..208....5N }}</ref>

==Effects from physical optics or radiative transfer==
The interactions and phenomena summarised in the subjects of [[radiative transfer]] and [[physical optics]] can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases, the shifts correspond to a physical energy transfer to matter or other photons rather than being by a transformation between reference frames. Such shifts can be from such physical phenomena as [[Wolf effect|coherence effects]] or the [[scattering]] of [[electromagnetic radiation]] whether from [[electric charge|charged]] [[elementary particle]]s, from [[particulates]], or from fluctuations of the [[index of refraction]] in a [[dielectric]] medium as occurs in the radio phenomenon of [[Whistler (radio)|radio whistlers]].<ref name="basicastronomy"/> While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the [[#Redshift formulae|effects discussed above]].<ref name="basicastronomy"/>

In many circumstances scattering causes radiation to redden because [[entropy]] results in the predominance of many low-[[energy]] photons over few high-energy ones (while [[conservation of energy|conserving total energy]]).<ref name="basicastronomy"/> Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated {{math|''z''}} is generally a [[function (mathematics)|function]] of wavelength. Furthermore, scattering from [[randomness|random]] [[matter|media]] generally occurs at many [[angle]]s, and {{math|''z''}} is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of [[spectral line]]s as well.<ref name="basicastronomy"/>

In [[interstellar medium|interstellar astronomy]], [[Visible spectrum|visible spectra]] can appear redder due to scattering processes in a phenomenon referred to as [[interstellar reddening]]<ref name="basicastronomy"/>—similarly [[Rayleigh scattering]] causes the [[Atmosphere of Earth|atmospheric]] reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue colour. This phenomenon is distinct from redshifting because the [[spectroscopic]] lines are not shifted to other wavelengths in reddened objects and there is an additional [[extinction (astronomy)|dimming]] and distortion associated with the phenomenon due to photons being scattered in and out of the [[Line-of-sight propagation|line of sight]].<ref>{{Cite web |last=Impey |first=Chris |editor-last=Gay |editor-first=Pamela |title=Dust Extinction and Reddening |url=https://www.teachastronomy.com/textbook/The-Milky-Way/Dust-Extinction-and-Reddening/ |access-date=2025-03-06 |website=Dust Extinction and Reddening |publisher=Teach Astronomy |language=en}}</ref>

==Blueshift==
{{redirect|Blueshift|the term as used in photochemistry|hypsochromic shift|the political phenomenon|blue shift (politics)|other uses of "blueshift" or "blue shift"}}
The opposite of a redshift is a '''blueshift'''. A blueshift is any decrease in [[wavelength]] (increase in [[energy]]), with a corresponding increase in frequency, of an [[electromagnetic wave]]. In [[Light|visible light]], this shifts a color towards the blue end of the spectrum.

=== Doppler blueshift ===
[[File:Redshift blueshift.svg|thumb|Doppler redshift and blueshift]]
[[Doppler effect|Doppler]] blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the [[visible spectrum]]. Only objects moving at near-[[relativistic speed]]s toward the observer are noticeably bluer to the [[naked eye]], but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.<ref>{{cite book|title=In Quest of the Universe | first1=Karl F. | last1=Kuhn | first2=Theo | last2=Koupelis |year= 2004|publisher=[[Jones & Bartlett Publishers]]|isbn=978-0-7637-0810-8|pages=122–3}}</ref>

Doppler blueshift is used in [[astronomy]] to determine relative motion:
* The [[Andromeda Galaxy]] is moving toward our own [[Milky Way]] [[galaxy]] within the [[Local Group]]; thus, when observed from Earth, its light is undergoing a blueshift.<ref>{{cite book |last=Woodhouse |first=Chris |chapter=M31 (Andromeda Galaxy) |date=2017-12-04 |title=The Astrophotography Manual |pages=308–313 |edition=2nd |publisher=Routledge |language=en |doi=10.4324/9781315159225-42 |isbn=978-1-315-15922-5}}</ref>
* Components of a [[binary star]] system will be blueshifted when moving towards Earth
* When observing spiral galaxies, the side spinning toward us will have a slight blueshift ''relative to'' the side spinning away from us (see [[Tully–Fisher relation]]).
* [[Blazar]]s are known to propel [[relativistic jet]]s toward us, emitting [[synchrotron radiation]] and [[bremsstrahlung]] that appears blueshifted.<ref>{{Cite book |arxiv=2412.11565 |doi=10.69646/aob104p029 |chapter=Monitoring Blazar Variability to Understand Extragalactic Jets |title=Publications of the Astronomical Observatory of Belgrade |date=2024 |last1=Maria Raiteri |first1=Claudia |volume=104 |pages=29–38 |isbn=978-86-82296-11-9 }}</ref>
* Nearby stars such as [[Barnard's Star]] are moving toward us, resulting in a very small blueshift.
* Doppler blueshift of distant objects with a high ''z'' can be subtracted from the much larger [[Hubble's law|cosmological redshift]] to determine relative motion in the [[Metric expansion of space|expanding universe]].<ref name="Aoki2005">{{cite journal | title = The Largest Blueshifts of the [O III] Emission Line in Two Narrow-Line Quasars | journal = Astrophysical Journal | date = January 2005 | first1=Kentaro | last1=Aoki | first2=Toshihiro | last2=Kawaguchi | first3=Kouji | last3=Ohta | volume = 618 | issue = 2 | pages = 601–608 |arxiv = astro-ph/0409546 |bibcode = 2005ApJ...618..601A |doi = 10.1086/426075 | s2cid = 17680991 }}</ref>

=== Gravitational blueshift ===
[[Image:Gravitional well.jpg|thumb|[[Matter waves]] (protons, electrons, photons, etc.) falling into a [[gravity well]] become more energetic and undergo observer-independent blueshifting.]]
Unlike the ''relative'' Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is ''absolute'' and does not depend on the received angle of the photon:

{{Blockquote|Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.<ref name=R.N_1>{{cite web| first=R. J. | last=Nemiroff| title=Gravitational Principles and Mathematics| url=http://antwrp.gsfc.nasa.gov/htmltest/gifcity/nslens_math.html| date=1993| publisher=[[NASA]]}}</ref><ref name=R.N_2>{{cite journal| first=R. J. | last=Nemiroff| title=Visual distortions near a neutron star and black hole| date=1993| journal=American Journal of Physics| volume=61| issue=7| pages=619–632| bibcode=1993AmJPh..61..619N| doi=10.1119/1.17224| arxiv=astro-ph/9312003v1| s2cid=16640860}}</ref>}}

It is a natural consequence of [[conservation of energy]] and [[mass–energy equivalence]], and was confirmed experimentally in 1959 with the [[Pound–Rebka experiment]]. Gravitational blueshift contributes to [[cosmic microwave background]] (CMB) anisotropy via the [[Sachs–Wolfe effect]]: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of [[gravitational redshift]] as it leaves the region.<ref name="Bonometto2002">{{cite book | last1 = Bonometto | first1 = Silvio | last2 = Gorini | first2 = Vittorio | last3 = Moschella | first3 = Ugo | title = Modern Cosmology | publisher = [[CRC Press]] | date = 2002 | isbn = 978-0-7503-0810-6 }}</ref>

==== Blue outliers ====
There are far-away [[active galaxies]] that show a blueshift in their [[Doubly ionized oxygen|[O III]]] emission [[Emission spectrum|lines]]. One of the largest blueshifts is found in the narrow-line [[quasar]], [[PG 1543+489]], which has a relative velocity of −1150&nbsp;km/s.<ref name="Aoki2005" /> These types of galaxies are called "blue outliers".<ref name="Aoki2005" />

===Cosmological blueshift===
In a hypothetical universe undergoing a runaway [[Big Crunch]] contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed [[cosmological redshift]] in the present [[expanding universe]].<ref>{{Cite web |last=Miller |first=Cole |title=Cosmology |url=https://www.astro.umd.edu/~miller/teaching/questions/cosmology.html |access-date=2025-03-06 |website=www.astro.umd.edu}}</ref>

==See also==
* [[Gravitational potential]]
* [[Mattig formula]]
* [[Relativistic Doppler effect]]

==References==
{{Reflist}}

==Sources==
===Articles===
* Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in ''Sky & Telescope'' Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)
* Lineweaver, Charles H. and Tamara M. Davis, "[https://web.archive.org/web/20070715030354/http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147 Misconceptions about the Big Bang]", ''[[Scientific American]]'', March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)

===Books===
* {{cite book | last=Nussbaumer|first=Harry|author2=Lydia Bieri |author2-link=Lydia Bieri|title=Discovering the Expanding Universe|publisher=Cambridge University Press|date=2009|isbn=978-0-521-51484-2}}
* {{cite book | last1=Binney|first1=James |author-link=James Binney|first2=Michael |last2=Merrifeld |title=Galactic Astronomy|publisher=Princeton University Press|date=1998|isbn=978-0-691-02565-0}}
* {{cite book | last1=Carroll |first1=Bradley W. | first2=Dale A. |last2=Ostlie | name-list-style=amp| title=An Introduction to Modern Astrophysics| publisher=Addison-Wesley | date=1996| isbn=978-0-201-54730-6}}
* {{cite book | author=[[Richard Feynman|Feynman, Richard]] | author2=[[Robert B. Leighton|Leighton, Robert]] | author3=[[Matthew Sands|Sands, Matthew]] | title=Feynman Lectures on Physics |volume=1 | publisher=Addison-Wesley | date=1989 | isbn=978-0-201-51003-4| title-link=The Feynman Lectures on Physics }}
* {{cite book | last1 = Grøn | first1 = Øyvind |author-link1=Øyvind Grøn|last2=Hervik |first2=Sigbjørn | title = Einstein's General Theory of Relativity | location = New York | publisher = Springer | date = 2007 | isbn = 978-0-387-69199-2}}
* {{cite book |last=Harrison |first=Edward |author-link=Edward Robert Harrison |date=2000 |title=Cosmology: The Science of the Universe |edition=2nd |publisher=Cambridge University Press |isbn=978-0-521-66148-5}}
* {{cite book | last=Kutner |first=Marc | title=Astronomy: A Physical Perspective | url=https://archive.org/details/astronomyphysica00kutn | url-access=registration | publisher=Cambridge University Press | date=2003 | isbn=978-0-521-52927-3}}
* {{cite book | last1 = Misner | first1 = Charles | last2 = Thorne |first2 = Kip S. |author2-link = Kip Thorne | last3 = Wheeler |first3 = John Archibald | title = Gravitation | location = San Francisco | publisher = W. H. Freeman | date = 1973 | isbn = 978-0-7167-0344-0}}
* {{cite book | first = P. J. E. | last = Peebles |author-link=P. J. E. Peebles |title = Principles of Physical Cosmology | publisher = Princeton University Press | date = 1993 | isbn = 978-0-691-01933-8 | url = https://archive.org/details/principlesofphys00pjep }}
* {{cite book | title=Spacetime Physics: Introduction to Special Relativity | edition=2nd | publisher=W. H. Freeman | date=1992 | isbn=978-0-7167-2327-1 | last1=Taylor | first1=Edwin F. | last2=Wheeler | first2=John Archibald | author-link2=John Archibald Wheeler | url=https://archive.org/details/spacetimephysics00edwi_0 }}
* {{cite book | first = Steven | last = Weinberg |author-link=Steven Weinberg | title = Gravitation and Cosmology | publisher = John Wiley | date = 1971 | isbn = 978-0-471-92567-5 | url = https://archive.org/details/gravitationcosmo00stev_0 }}
* See also {{section link|Physical cosmology#Textbooks}} for applications of the cosmological and gravitational redshifts.

==External links==
{{commons}}
{{wiktionary}}
* [http://www.astro.ucla.edu/~wright/doppler.htm Ned Wright's Cosmology tutorial]
* [https://web.archive.org/web/20051203093117/http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/redshift.html Cosmic reference guide entry on redshift]
* [https://web.archive.org/web/20051121214031/http://www.asterism.org/tutorials/tut29-1.htm Mike Luciuk's Astronomical Redshift tutorial]
* [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/Images/hu_animexp.gif Animated GIF of Cosmological Redshift] by Wayne Hu
* {{cite web|last1=Merrifield|first1=Michael|last2=Hill|first2=Richard|title=Z Redshift|url=http://www.sixtysymbols.com/videos/redshift.htm|work=SIXTψ SYMBΦLS|date=2009|publisher=[[Brady Haran]] for the [[University of Nottingham]]}}

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[[Category:Astronomical spectroscopy]]
[[Category:Doppler effects]]
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[[Category:Physical cosmology]]
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