De-Sitter model

The De-Sitter-Model (also De-Sitter-Kosmos ) is a space-time with positive cosmological constants and vanishing matter content . It was developed in 1917 by the Dutch astronomer Willem de Sitter and also introduced independently by Tullio Levi-Civita (1917). At that time, it was seen as a stationary universe and was the dominant cosmological model together and in competition with the Einstein cosmos until the early 1930s . It was later recognized as a special case of the dynamic Friedmann solutions . Due to the absence of matter, the de-sitter cosmos cannot fulfill Mach's principle . ${\displaystyle \Lambda >0}$ ${\displaystyle \rho =0}$

Depending on the choice of coordinates, there are different representations of the De-Sitter universe, so that in some representations it initially appeared as stationary:

• If you choose a Friedmann solution with vanishing curvature ( in the Robertson-Walker metric ) and without matter, the result is a flat, expanding De-Sitter cosmos with a radius and the Hubble constant . ${\displaystyle k=0}$ ${\displaystyle R(t)\sim e^{Ht}}$ ${\displaystyle H={\sqrt {\tfrac {\Lambda }{3}}}}$
• Both Friedmann solutions with have constant positive and negative curvature. ${\displaystyle k=\pm 1}$

In the opinion of many cosmologists, the universe initially resembled a de-sitter space (see inflation ). In the course of time, through the acceleration of the cosmic expansion and the thinning of matter caused by it, the universe could again approach such a matter-free model with cosmological constants.

history

The De-Sitter model was also historically important because it predicted an increase in the redshift of the galaxies with distance. Because of the First World War, de Sitter was not yet familiar with the data collected, in particular by Vesto Slipher , and was unable to make detailed comparisons with the observations, but the redshifts of the galaxies observed in increasing numbers in the 1920s were an argument for de Sitter's model and against Einstein's model of the non-expanding or contracting, static, unstable universe with respect to small changes. Due to this prediction, the De-Sitter theory influenced the thinking of Edwin Hubble , who interpreted his observations with the De-Sitter model in 1929.

Math

The (3,1) -dimensional spacetime of the de-sitter model is mathematically the special case of a de-sitter space , which is generally referred to as the ( d −1,1) -dimensional hypersphere of a ( d , 1) -dimensional flat Minkowski Space is defined. For mathematical details, see the De-Sitter room . A “counterpart” to the de-sitter space that has become particularly important in string theory is the anti-de-sitter space .

See also

• De-sitter room
• Anti-de-sitter room

Web links

• Marcus Spradlin, Andrew Strominger, Anastasia Volovich: Les Houches Lectures on De Sitter Space . In: arXiv. High Energy Physics - Theory . September 30, 2001, arxiv : hep-th / 0110007 .
• Stefan Röhle Mathematical Problems in the Einstein-De-Sitter Controversy , Preprint, MPI Berlin, on History (PDF; 1.5 MB)

Individual evidence

1. ^ W. de Sitter: On the relativity of inertia. Remarks concerning Einstein's latest hypothesis . In: Koninklijke Nederlandse Akademie van Weteschappen Proceedings Series B Physical Sciences . tape 19 , 1917, pp. 1217-1225 ( PDF ).
2. ↑ Steven Weinberg: Gravitation and Cosmology. Principles and applications of the general theory of relativity . Wiley 1972, p. 615.
3. ^ Norbert Straumann: The history of the cosmological constant problem . In: arXiv. Gravitation and Cosmology . August 13, 2002, arxiv : gr-qc / 0208027 .
4. ↑ Hubble wrote of the de-sitter theory: In its time it made a significant contribution to drawing attention to the possibility of a variable K-value (by which he meant the concept of the variability of the redshift with distance), cf. Edwin Hubble: In the realm of fog. Vieweg 1938, p. 101. The work of Carl Wilhelm Wirtz , who introduced the K-value in 1918 and continued to pursue a distance dependency in the context of the De-Sitter model in the 1920s, deserves special mention here.