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Expansion of space

In the earlier part of the twentieth century, Slipher, Wirtz and others made the first measurements of the redshifts and blueshifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blueshifts as being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to Einstein's equations of general relativity. The correlation between redshifts and distances arises in all expanding models.

This cosmological redshift is commonly attributed to stretching of the wavelengths of photons propagating through the expanding space. This interpretation can be misleading, however; expanding space is only a choice of coordinates and thus cannot have physical consequences. The cosmological redshift is more naturally interpreted as a Doppler shift arising due to the recession of distant objects.

The observational consequences of this effect can be derived using the equations from general relativity that describe a homogeneous and isotropic universe. The cosmological redshift can thus be written as a function of a, the time-dependent cosmic scale factor:

In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing as time passes, thus, z is positive and distant galaxies appear redshifted.

Using a 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 Ω:

with ρ 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. At large redshifts, 1 + z > Ω, one finds:

where H is the present-day Hubble constant, and z is the redshift.

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.