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This is a simple question of understanding. Would a de Sitter universe show cosmic background radiation? (After all, it is often explained said that our universe is similar to a de Sitter universe.)

Or is the observation of CBR a proof that we do NOT live in such a space?

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A small value of the cosmological constant(vacuum energy) is the simplest source of dark energy, and indicates that we live in a asymptotically de Sitter universe.

This means that our Universe asymptotes to a de Sitter space.

De Sitter space is the maximally symmetric solution of the vacuum Einstein equations with a cosmological constant (curvature).

An observer in a de Sitter space is surrounded by a cosmological horizon. The horizon is observer dependent.

No, the observation of CBR is not proof that we do not live in such a space.

You are correct, our universe is similar to (asymptotically approaches) a de Sitter universe.

Our universe has CMB, and asymptotically approaches a de Sitter space, but that is not necessarily always true the way around. Not all de Sitter spaces would have CMB.

https://en.wikipedia.org/wiki/De_Sitter_space

https://www.newton.ac.uk/files/seminar/20120626161516302-153120.pdf

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  • $\begingroup$ The two links say nothing about cosmic background radiation in de Sitter space. Is there more to read about this combined topic? I do not seem to find anything on scholar.google.com ... $\endgroup$ – frauke Sep 29 '19 at 12:16
  • $\begingroup$ @frauke yes please see these ones: arxiv.org/pdf/1412.4965.pdf arxiv.org/abs/astro-ph/0411579 $\endgroup$ – Árpád Szendrei Sep 29 '19 at 15:28

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