De Sitter universe

The de Sitter model (also de Sitter universe ) is a spacetime with positive cosmological constant and vanishing matter content. It was developed in 1917 by the Dutch astronomer Willem de Sitter and introduced independently by Tullio Levi -Civita (1917 ). At that time it was seen as a stationary universe and was until the early 1930s, together and in competition with the Einstein cosmos, the dominant cosmological model. Later it was recognized as a special case of the dynamic Friedmann solutions. Due to the absence of matter the de Sitter universe can not satisfy Mach's principle.

Depending on the choice of the coordinates are different representations of the de Sitter universe, so it initially appeared to be stationary in some representations:

• If one chooses a Friedmann solution with vanishing curvature ( in the Robertson - Walker metric ) and without matter, is obtained as the solution of a flat, of expanding de Sitter universe with radius and the Hubble constant.
• The two solutions have constant positive or negative curvature.

According to many cosmologists resembled the universe at the beginning of a de Sitter space (see inflation). Over time, the universe could be similar to such a matter-free model with cosmological constant again by the acceleration of the cosmic expansion and the dilution caused by it of matter.

History

Historically, the importance of the de Sitter model was also because it predicted an increase in the redshift of the galaxies with distance. Due to the First World War had known de Sitter was not yet the collated particular Vesto Slipher data and could no detailed comparisons with the observations do, but were observed in the 1920s in an increasing number of redshifts of galaxies then an argument for de Sitter model and against Einstein. Had the de Sitter theory due to these forecasts, influence on the thinking of Edwin Hubble, who interpreted his observations in 1929 with the de Sitter model.

Mathematical

The (3,1 )-dimensional spacetime of the de Sitter model is mathematically the special case of a de Sitter space, the generally flat as a (d- 1, 1 )-dimensional hypersphere of a (d, 1 )-dimensional Minkowski defined space. A particularly in string theory to meaning spillage of " counterpart " to the de Sitter space is the anti- de Sitter space.