- De Sitter universe
A

**de Sitter universe**is a solution to Einstein's field equations ofGeneral Relativity which is named afterWillem de Sitter . It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by thecosmological constant , thought to correspond todark energy .**Mathematical Expression**A de Sitter universe has no ordinary matter content but with a positive

cosmological constant which sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate::

$H\; propto\; frac\{sqrt\{Lambda\{M\_\{pl$,where the constants of proportionality depend on conventions. The cosmological constant is $Lambda$ and $M\_\{pl\}$ is the

Planck mass .It is common to describe a patch of this solution as an expanding universe of the FLRW form where the scale factor is given by:

:

$a(t)\; =\; e^\{Ht\}\; ,$,where the constant "H" is the Hubble expansion rate and "t" is time. As in all FLRW spaces, $a(t)$, the scale factor, describes the expansion of physical spatial distances.

**Our universe is becoming like de Sitter universe**Because our Universe has entered the

Dark Energy Dominated Era a few billion years ago, our universe is probably approaching a de Sitter universe in the infinite future. If the current acceleration of our universe is due to a cosmological constant then as the universe continues to expand all of the matter and radiation will be diluted. Eventually there will be almost nothing left but the cosmological constant, and our universe will have become a de Sitter universe.**Acceleration becomes faster than light**The exponential expansion of the scale factor means that the physical distance between any two non-accelerating observers will eventually be growing faster than the

speed of light . At this point those two observers will no longer be able to make contact. Therefore any observer in a de Sitter universe would seeevent horizon s beyond which that observer can never see nor learn any information. If our universe is approaching a de Sitter universe then eventually we will not be able to observe any galaxies other than our ownMilky Way and a few others in the gravitationally boundLocal Group .**Modelling cosmic inflation**Another application of de Sitter space is in the

early universe duringcosmic inflation . Many inflationary models are approximately de Sitter space and can be modeled by giving the Hubble parameter a mild time dependence. For simplicity, some calculations involving inflation in the early universe can be performed in de Sitter space rather than a more realistic inflationary universe. By using the de Sitter universe instead, where the expansion is truly exponential, there are many simplifications.**ee also***

Cosmic inflation

*Deceleration parameter

*De Sitter space for more mathematical properties**References**#An Introduction to General Relativity by Ronald Adler, Maurice Bazin, and Menahem Schiffer

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**de Sitter universe**— Physical cosmology Universe · Big Bang … Wikipedia**Sitter, Willem de**— ▪ Dutch mathematician and astronomer born May 6, 1872, Sneek, Neth. died Nov. 20, 1934, Leiden Dutch mathematician, astronomer, and cosmologist who developed theoretical models of the universe based on Albert Einstein s general theory of… … Universalium**Universe**— For other uses, see Universe (disambiguation). Physical cosmology … Wikipedia**de Sitter invariant special relativity**— In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the Indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of General… … Wikipedia**de Sitter space**— In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n dimensional de Sitter space , denoted dSn, is the Lorentzian manifold analog of an n sphere (with its… … Wikipedia**De Sitter , Willem**— (1872–1934) Dutch astronomer and mathematician De Sitter, the son of a judge from Leiden in the Netherlands, studied mathematics and physics at the University of Groningen, his interest in astronomy being aroused by Jacobus Kapteyn. After serving … Scientists**De Sitter space**— In mathematics and physics, n dimensional De Sitter space, denoted dS n, is the Lorentzian analog of an n sphere (with its canonical Riemannian metric). It is a maximally symmetric, Lorentzian manifold with constant positive curvature, and is… … Wikipedia**Willem de Sitter**— de Sitter redirects here. For other uses, see Sitter (disambiguation). Willem de Sitter Born 6 May 1872(1872 05 06 … Wikipedia**de Sitter–Schwarzschild metric**— In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. Unlike a flat space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime. The Nariai… … Wikipedia**De Sitter effect**— In astrophysics, the term De Sitter effect (named after the Dutch physicist Willem de Sitter) has been applied to two unrelated phenomena. The De Sitter effect was first described by de Sitter in 1913 and used to support the special theory of… … Wikipedia