# Hubble's law

Hubble's law, also known as the Hubble–Lemaître law,[1] is the observation in physical cosmology that:

1. Objects observed in deep space—extragalactic space, 10 megaparsecs (Mpc) or more—are found to have a redshift, interpreted as a relative velocity away from Earth;
2. This Doppler shift-measured velocity of various galaxies receding from the Earth is approximately proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away.[2][3]

Hubble's law is considered the first observational basis for the expansion of the universe and today serves as one of the pieces of evidence most often cited in support of the Big Bang model.[4][5]The motion of astronomical objects due solely to this expansion is known as the Hubble flow.[6]

Although widely attributed to Edwin Hubble,[7][8][9] the law was first derived from the general relativity equations in 1922 by Alexander Friedmann. Friedmann published a set of equations, now known as the Friedmann equations, showing that the universe might expand, and presenting the expansion speed if this was the case.[10] Then Georges Lemaître, in a 1927 article, proposed the expansion of the universe and suggested an estimated value of the rate of expansion, which when corrected by Hubble became known as the Hubble constant.[4][11][12][13] However, though the Hubble constant ${\displaystyle H_{0}}$ is roughly constant in the velocity-distance space at this moment in time, the Hubble parameter ${\displaystyle H}$, which the Hubble constant is the current value of, changes with time, so the term 'constant' is sometimes thought of as somewhat of a misnomer. Moreover, two years later Edwin Hubble confirmed the existence of cosmic expansion, and determined a more accurate value for the constant that now bears his name.[14]Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917.[15][16][17][18] In October 2018, scientists presented a new third way (two earlier methods gave problematic results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the exact rate of expansion of the universe.[19][20]

The law is often expressed by the equation v = H0D, with H0 the constant of proportionality—Hubble constant—between the "proper distance" D to a galaxy, which can change over time, unlike the comoving distance, and its velocity v, i.e. the derivative of proper distance with respect to cosmological time coordinate. (See uses of the proper distance for some discussion of the subtleties of this definition of 'velocity'.) Also, the SI unit of H0 is s−1, but it is most frequently quoted in (km/s)/Mpc, thus giving the speed in km/s of a galaxy 1 megaparsec (3.09×1019 km) away. The reciprocal of H0 is the Hubble time.

## Observed values of the Hubble constant

Date published Hubble constant
(km/s)/Mpc
Observer Citation Remarks / methodology
2018-11-06 67.77±1.30 DES Collaboration [21] Supernova measurements using the inverse distance ladder method based on baryon acoustic oscillations.
2018-09-05 72.5+2.1
−2.3
H0LiCOW collaboration [22] Observations of multiply imaged quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
2018-07-18 67.66±0.42 Planck Mission [23] Final Planck 2018 results.
2018-04-27 73.52±1.62 Hubble Space Telescope and Gaia [24][25] Additional HST photometry of galactic Cepheids with early Gaia parallax measurements. The revised value increases tension with CMB measurements at the 3.8σ level. Continuation of a collaboration known as Supernovae, ${\displaystyle H_{0}}$, for the Equation of State of Dark Energy (SHoES).
2018-02-22 73.45±1.66 Hubble Space Telescope [26][27] Parallax measurements of galactic Cepheids for enhanced calibration of the distance ladder; the value suggests a discrepancy with CMB measurements at the 3.7σ level. The uncertainty is expected to be reduced to below 1% with the final release of the Gaia catalog. SHoES collaboration.
2017-10-16 70.0+12.0
−8.0
The LIGO Scientific Collaboration and The Virgo Collaboration [28] Measurement was independent of a cosmic ‘distance ladder'; the gravitational-wave analysis of a binary neutron star (BNS) merger GW170817 directly estimated the luminosity distance out to cosmological scales. An estimate of fifty similar detections in the next decade may arbitrate tension of other methodologies.[29] Detection and analysis of a neutron star-black hole merger (NSBH) may provide greater precision than BNS could allow.[30]
2016-11-22 71.9+2.4
−3.0
Hubble Space Telescope [31] Uses time delays between multiple images of distant variable sources produced by strong gravitational lensing. Collaboration known as ${\displaystyle H_{0}}$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW).
2016-07-13 67.6+0.7
−0.6
SDSS-III Baryon Oscillation Spectroscopic Survey [32] Baryon acoustic oscillations. An extended survey (eBOSS) began in 2014 and is expected to run through 2020. The extended survey is designed to explore the time when the universe was transitioning away from the deceleration effects of gravity from 3 to 8 billion years after the Big Bang.[33]
2016-05-17 73.24±1.74 Hubble Space Telescope [34] Type Ia supernova, the uncertainty is expected to go down by a factor of more than two with upcoming Gaia measurements and other improvements. SHoES collaboration.
2015-02 67.74±0.46 Planck Mission [35][36] Results from an analysis of Planck's full mission were made public on 1 December 2014 at a conference in Ferrara, Italy. A full set of papers detailing the mission results were released in February 2015.
2013-10-01 74.4±3.0 Cosmicflows-2 [37] Comparing redshift to other distance methods, including Tully–Fisher, Cepheid variable, and Type Ia supernovae.
2013-03-21 67.80±0.77 Planck Mission [38][39][40][41][42] The ESA Planck Surveyor was launched in May 2009. Over a four-year period, it performed a significantly more detailed investigation of cosmic microwave radiation than earlier investigations using HEMT radiometers and bolometer technology to measure the CMB at a smaller scale than WMAP. On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission's data including a new CMB all-sky map and their determination of the Hubble constant.
2012-12-20 69.32±0.80 WMAP (9 years), combined with other measurements. [43]
2010 70.4+1.3
−1.4
WMAP (7 years), combined with other measurements. [44] These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data are fit with more general versions, H0 tends to be smaller and more uncertain: typically around 67±4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc.[45]
2010 71.0±2.5 WMAP only (7 years). [44]
2009-02 70.5±1.3 WMAP (5 years), combined with other measurements. [46]
2009-02 71.9+2.6
−2.7
WMAP only (5 years) [46]
2007 70.4+1.5
−1.6
WMAP (3 years), combined with other measurements. [47]
2006-08 76.9+10.7
−8.7
Chandra X-ray Observatory [48] Combined Sunyaev–Zel'dovich effect and Chandra X-ray observations of galaxy clusters. Adjusted uncertainty in table from Planck Collaboration 2013.[49]
2001-05 72±8 Hubble Space Telescope Key Project [50] This project established the most precise optical determination, consistent with a measurement of H0 based upon Sunyaev–Zel'dovich effect observations of many galaxy clusters having a similar accuracy.
prior to 1996 50–90 (est.) [51]
early 1970s ~55 (est.) Allan Sandage and Gustav Tammann [52]
1958 75 (est.) Allan Sandage [53] This was the first good estimate of H0, but it would be decades before a consensus was achieved.
1956 180 Humason, Mayall and Sandage [52]
1929 500 Edwin Hubble, Hooker telescope [54][52][55]
1927 625 Georges Lemaître [56] First measurement and interpretation as a sign of the expansion of the universe
Estimated values of the Hubble constant, 2001–2018. Estimates with circles represent calibrated distance ladder measurements, squares represent early universe CMB/BAO measurements with ΛCDM parameters while triangles are independent measurements.
Other Languages
Afrikaans: Wet van Hubble
العربية: قانون هابل
asturianu: Llei de Hubble
azərbaycanca: Habbl qanunu
беларуская: Закон Хабла
български: Закон на Хъбъл
bosanski: Hubbleov zakon
español: Ley de Hubble
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hrvatski: Hubbleov zakon
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italiano: Legge di Hubble
עברית: חוק האבל
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latviešu: Habla likums
Lëtzebuergesch: Hubble-Konstant
lietuvių: Hablo dėsnis
Bahasa Melayu: Hukum Hubble
occitan: Lei de Hubble
پنجابی: ہبل دا قنون
русский: Закон Хаббла
sicilianu: Liggi di Hubble
Simple English: Hubble's law
slovenčina: Hubblov zákon
slovenščina: Hubblov zakon
српски / srpski: Hablov zakon
srpskohrvatski / српскохрватски: Hablov zakon
svenska: Hubbles lag
татарча/tatarça: Habbl qanunı
Türkçe: Hubble kanunu
українська: Закон Габбла
Tiếng Việt: Định luật Hubble
West-Vlams: Wet van Hubble