Is the de Sitter Universe equivalent to the static Einstein Universe?

Question

The de Sitter universe is a flat exponentially expanding universe with a cosmological constant $\Lambda$ and no matter.

Einstein's static universe also has a cosmological constant $\Lambda$ but it also has matter and it is static. Can we make some coordinate transformation to the de Sitter universe to show equivalence of the universes?

No, they aren't equivalent. For a start the de Sitter universe is open while the Einstein static universe can be open or closed. — John Rennie, Sep 18 '17 at 11:11
Are you sure that you are not interpreting the Einstein-de Sitter universe as equivalence of the de Sitter universe and Einstein universe? — Immanuel, Sep 18 '17 at 11:40

score 1 · Accepted Answer · edited Jun 04 '20 at 16:03

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The de Sitter universe is a [...] universe with [...] no matter.

Einstein's static universe [...] has matter

Can we make some coordinate transformation to the de Sitter universe to show equivalence of the universes?

Coordinate transformations cannot change the zero energy-momentum tensor of a de Sitter universe into the non-zero energy-momentum tensor of an Einstein uiverse.

edited Jun 04 '20 at 16:03

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answered Sep 18 '17 at 13:45

Christoph

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Is the de Sitter Universe equivalent to the static Einstein Universe?

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