- De Sitter universe
A de Sitter universe is a solution to Einstein's field equations of
General Relativitywhich is named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy.
A de Sitter universe has no ordinary matter content but with a positive
cosmological constantwhich sets the expansion rate, H. A larger cosmological constant leads to a larger expansion rate:
where the constants of proportionality depend on conventions. The cosmological constant is and is the
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:
Our universe is becoming like de Sitter universe
Because our Universe has entered the
Dark Energy Dominated Eraa 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 see event horizons 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 own Milky Wayand a few others in the gravitationally bound Local Group.
Modelling cosmic inflation
Another application of de Sitter space is in the
early universeduring cosmic 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.
De Sitter spacefor more mathematical properties
#An Introduction to General Relativity by Ronald Adler, Maurice Bazin, and Menahem Schiffer
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