Expansion of space
Main article: Metric expansion of space
In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blue shifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blue shifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. Hubble's law of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a metric expansion of space.[16] As a result, photons propagating through the expanding space are stretched, creating the cosmological redshift. This differs from the Doppler effect redshifts described above because the velocity boost (i.e. the Lorentz transformation) between the source and observer is not due to classical momentum and energy transfer, but instead the photons increase in wavelength and redshift as the space through which they are traveling expands.[22] This effect is prescribed by the current cosmological model as an observable manifestation of the time-dependent cosmic scale factor (a) in the following way:
[equation in original]
This type of redshift is called the cosmological redshift or Hubble redshift. If the universe were contracting instead of expanding, we would see distant galaxies blue shifted by an amount proportional to their distance instead of redshifted.[23]
These galaxies are not receding simply by means of a physical velocity in the direction away from the observer; instead, the intervening space is stretching, which accounts for the large-scale isotropy of the effect demanded by the cosmological principle.[24] For cosmological redshifts of z < 0.1 the effects of spacetime expansion are minimal and observed redshifts dominated by the peculiar motions of the galaxies relative to one another that cause additional Doppler redshifts and blue shifts.[25] The difference between physical velocity and space expansion can be illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched. (Obviously, there are dimensional problems with the model, as the ball bearings should be in the sheet, and cosmological redshift produces higher velocities than Doppler does if the distance between two objects is large enough.)
In spite of the distinction between redshifts caused by the velocity of objects and the redshifts associated with the expanding universe, astronomers sometimes refer to "recession velocity" in the context of the redshifting of distant galaxies from the expansion of the Universe, even though it is only an apparent recession.[26] As a consequence, popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the motion of galaxies dominated by the expansion of spacetime, despite the fact that a "cosmological recessional speed" when calculated will not equal the velocity in the relativistic Doppler equation.[27] In particular, Doppler redshift is bound by special relativity; thus v > c is impossible while, in contrast, v > c is possible for cosmological redshift because the space which separates the objects (e.g., a quasar from the Earth) can expand faster than the speed of light.[28] More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing coordinate systems. Expressing this precisely requires working with the mathematics of the Friedmann-Robertson-Walker metric.[29]