Cosmological Distance Measure

Read here about Cosmological Distance Measure, the methods by which traditional units of distance (eg. meters) are extrapolated to account for phenomena of cosmological size, ie. groups of galaxies.

About Cosmological Distance Measure

Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some observable quantity (such as the luminosity of a distant quasar, the redshift of a distant galaxy, or the angular size of the acoustic peaks in the CMB power spectrum) to another quantity that is not directly observable, but is more convenient for calculations (such as the comoving coordinates of the quasar, galaxy, etc). The distance measures discussed here all reduce to the naïve notion of Euclidean distance at low redshift.
In accord with our present understanding of cosmology, these measures are calculated within the context of general relativity, where the Friedmann–Lemaitre–Robertson–Walker solution is used to describe the universe.

Major methods

  • Angular diameter distance is a good indication (especially in a flat universe) of how near an astronomical object was to us when it emitted the light that we now see. The angular diameter distance to an object is defined in terms of the object's actual size, x, and θ the angular size of the object as viewed from earth.
  • Luminosity distance. Luminosity distance DL is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object. For nearby objects (say, in the Milky Way) the luminosity distance gives a good approximation to the natural notion of distance in Euclidean space. The relation is less clear for distant objects like quasars far beyond the Milky Way since the apparent magnitude is affected by spacetime curvature, redshift, and time dilation. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship.
  • Comoving distance. The distance between two points measured along a path defined at the present cosmological time. In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, measured using a long series of rulers stretched out from our position to the object's position at that time, and which can change over time due to the expansion of the universe. Comoving distance factors out the expansion of the universe, giving a distance that doesn't change over time, though it is defined to be equal to the proper distance at the present time.
  • Cosmological proper distance. The distance between two points measured along a path defined at a constant cosmological time. The cosmological proper distance should not be confused with the more general proper length or proper distance.
  • Light travel time or lookback time. This is how long ago light left an object of given redshift.
  • Light travel distance (LTD). The light travel time times the speed of light. For values above 2 billion light years, this value does not equal the comoving distance or the angular diameter distance anymore, because of the expansion of the universe. Also see misconceptions about the size of the visible universe.
  • Naive Hubble's law, taking z = H0d/c, with H0 today's Hubble constant, z the redshift of the object, c the speed of light, and d the "distance."

Cosmic Distance Ladder

The cosmic distance ladder (also known as the Extragalactic Distance Scale) is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement to an astronomical object is only possible for those objects that are "close enough" (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances with methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity.
The ladder analogy arises because no one technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.