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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?

John Rennie
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Sergio
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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.

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Christoph
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