Hubble's law

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Hubble's law, also known as the Hubble–Lemaître law,^[1] is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther a galaxy is from the Earth, the faster it moves away. A galaxy's recessional velocity is typically determined by measuring its redshift, a shift in the frequency of light emitted by the galaxy.

The discovery of Hubble's law is attributed to work published by Edwin Hubble in 1929,^[2][3][4] but the notion of the universe expanding at a calculable rate was first derived from general relativity equations in 1922 by Alexander Friedmann. The Friedmann equations showed the universe might be expanding, and presented the expansion speed if that were the case.^[5] Before Hubble, astronomer Carl Wilhelm Wirtz had, in 1922^[6] and 1924,^[7] deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede faster from the observer. In 1927, Georges Lemaître concluded that the universe might be expanding by noting the proportionality of the recessional velocity of distant bodies to their respective distances. He estimated a value for this ratio, which—after Hubble confirmed cosmic expansion and determined a more precise value for it two years later—became known as the Hubble constant.^{[8][9][10][11][12]} 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.^[13][14][15] Combining Slipher's velocities with Henrietta Swan Leavitt's intergalactic distance calculations and methodology allowed Hubble to better calculate an expansion rate for the universe.^[16]

Hubble's law is considered the first observational basis for the expansion of the universe, and is one of the pieces of evidence most often cited in support of the Big Bang model.^[8][17] The motion of astronomical objects due solely to this expansion is known as the Hubble flow.^[18] It is described by the equation v = H₀D, with H₀ the constant of proportionality—the Hubble constant—between the "proper distance" D to a galaxy (which can change over time, unlike the comoving distance) and its speed of separation v, i.e. the derivative of proper distance with respect to the cosmic time coordinate.^[a] Though the Hubble constant H₀ is constant at any given moment in time, the Hubble parameter H, of which the Hubble constant is the current value, varies with time, so the term constant is sometimes thought of as somewhat of a misnomer.^[19][20]

The Hubble constant is most frequently quoted in km/s/Mpc, which gives the speed of a galaxy 1 megaparsec (3.09×10¹⁹ km) away as 70 km/s. Simplifying the units of the generalized form reveals that H₀ specifies a frequency (SI unit: s⁻¹), leading the reciprocal of H₀ to be known as the Hubble time (14.4 billion years). The Hubble constant can also be stated as a relative rate of expansion. In this form H₀ = 7%/Gyr, meaning that, at the current rate of expansion, it takes one billion years for an unbound structure to grow by 7%.

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