Astronomy & Celestial Mechanics
the sky, computed
Concept

Cosmological redshift — where it appears

The lengthening of light's wavelength by the expansion of the universe during its journey. One plus the redshift is the ratio of the scale factor when the light arrives to its value when the light left, not a velocity of the source.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The same recession law from two different galaxies. Twenty galaxies at fixed comoving positions after the whole picture has been multiplied by 1.34, with each galaxy's displacement drawn from where it was to where it is. Every arrow's tail sits at the old separation and its tip at the new one, so the arrow is exactly 0.34 times its tail's distance from the highlighted galaxy — proportional to separation for one reason and no other: a uniform scaling moves everything in proportion to its distance from whatever point the scaling is measured about. The right-hand panel measures from a different galaxy and gets the identical law with the identical constant. That is the content of a linear velocity–distance relation. It is the signature of an expansion with no centre, and the observation that every galaxy recedes is therefore not evidence that this one is the centre — it is evidence that none of them is.

The shift that is not a Doppler shift

Every galaxy beyond the Local Group has its lines shifted to the red, by an amount proportional to its distance. Read as a velocity that looks like a confession that everything is fleeing from here; read as a change of scale it says the opposite, because a uniform expansion produces exactly the same law measured from any galaxy in it.

cosmology · Expansion How much a galaxy's redshift changes in 10 years, and which way. The change in a galaxy's apparent recession velocity over 10 years of the observer's time, c ż/(1 + z), against the galaxy's redshift, for three universes with the same present expansion rate of 67.36 km/s/Mpc. The drift is (1 + z) H₀ − H(z): positive if the expansion rate at the galaxy's epoch was less than (1 + z) times today's, which is to say if the expansion has been accelerating since. In the empty universe the expansion rate is exactly (1 + z) H₀ at every epoch and nothing drifts at all. In the matter-only universe the expansion has only ever slowed, and every redshift falls: −8.6 cm/s over 10 years at z = 1 and −25.5 at z = 4. In ΛCDM the drift is positive nearby, largest at z = 0.63 where it reaches 2.51 cm/s, changes sign at z = 1.91, and is −5.5 cm/s at z = 4. The whole signal is a few centimetres per second in a decade, against the thirty kilometres per second of the Earth's own orbital motion that has to be removed from every spectrum first.

A redshift that changes while it is watched

A galaxy's redshift is a ratio of two sizes of the universe, and the second one is still growing while the light is being collected. So every redshift drifts, by a few centimetres per second in a decade, and the direction of the drift says whether the expansion has been speeding up since the light left — the one test of that question that needs no distance and no model of any source.

cosmology · Expansion

Named alongside it

The objects these essays reach for when they reach for this one.

Peculiar velocityScale factorComoving coordinatesComoving distanceConformal timeCosmic accelerationCosmological principleDark energyExpansion of spaceHubble lawHubble parameterThe Lyman-α forest

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