The universe of Sitter is an exact solution of the equations of the General relativity corresponding physically to a Univers Homogène, isotropic, vacuum of matter but filled of a Constante cosmological positive and noted here $\backslash \; Lambda$. It is a space of positive Courbure (being worth $4\; \backslash \; Lambda$) although its space Courbure can be unspecified. It bears the name of the physicist Willem de Sitter.

It enters the general class of solutions of the type FLRW. The Scale factor correspondent to this geometry is, by noting K the space curve being worth 1 (resp. 0 or -1) if the space curve is positive (resp. null or negative).

$\backslash \; frac\; \{has\; (T)\}\{a\_0\}\; =\; \backslash \; left\; \backslash \; \{\backslash \; begin\; \{matrix\}\; \backslash \; cosh\; (HT)\; \backslash ;\; if\; \backslash ;\; k=1\; \backslash \; \backslash \; \backslash \; exp\; (HT)\; \backslash ;\; if\; \backslash ;\; k=0\; \backslash \; \backslash \; \backslash \; sinh\; (HT)\; \backslash ;\; if\; \backslash ;\; k=-1\; \backslash \; \backslash \; \backslash end\{matrix\}\; \backslash \; right.$

where H is the Rate growth or Paramètre of Hubble and is here constant . It is connected to the cosmological constant by the relation.

$H=\; \backslash \; sqrt$

It is seen that for long times, $Ht>>1$, the distinction between the various space curves disappears. Actually, these three apparently different solutions can be seen like three frames of reference different from the same four-dimensional space (see Espace of Sitter for more mathematical details on this fact). This is due to ambiguity, from the point of view of total space with four dimensions, the separation made between the coordinate of time which plays the part of cosmic Temps and of the three space coordinates.

In a universe of Sitter the distance between observers comobiles grows so quickly that it is not possible for an observer to detect anything beyond distance $cH^\; \{-\; 1\}$ called particulate Horizon. In the same way an event cannot have of influence in any place located beyond of a distance $cH^\; \{-\; 1\}$ and one speaks in this case about Horizon about the events.

The universe of Sitter is the prototype of the geometries appearing within the framework of the cosmic Inflation. In these scenarios the value of the constant of Hubble H is not given by a cosmological constant but depends on the value of a field called Inflaton. It is roughly constant for one short period following the Big Bang thus leading to a geometry indeed of Sitter during this amount of time.

See too

• Space of Sitter
• anti Space of Sitter
• anti Universe of cosmic Sitter
• Inflation
• Willem de Sitter