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In this talk, the not yet settled down idea that the wave function of the universe could potentially be written as the partition function of a scale invariant statistical field theory is mentioned:

$$ \Psi[g] = Z[g] = \int D(\text{Fields}) e^{-S[g,\text{Fields}]} $$

If our universe were AdS, this relation could already be well enough explained by the AdS/CFT correspondence, but as our expanding universe correspond to a dS geometry, things are less clear.

What are the concrete technical arguments, ideas, or hints that this relationship should hold for our dS universe too? What work has already been done on this?

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Similar approaches have been generalized to more general spacetimes.

Technical details for dS space and further references in this paper about the holographic principle, p.43 ff., may provide some idea.

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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ – HDE 226868 Oct 22 '16 at 17:33
  • $\begingroup$ @HDE226868 I do not particularly appreciate it if other users (reviewers) who have contributed no topical content to the thread try to delete answers to my questions that contain valuable information. A link to a research-paper (the answer even says on which page I have to look) IS useful information that must not be deleted. I strongly disagree with the SE dogma that such answers are not useful to the asker and other people looking at the question! $\endgroup$ – Dilaton Oct 22 '16 at 20:10
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    $\begingroup$ @Dilaton Why don't you write up a self-answer to the question using the references? You'd likely be one of the more qualified people on Astronomy to write such an answer, and it would be extremely helpful; I have no doubt you could repackage the authors' work into something even clearer. $\endgroup$ – HDE 226868 Oct 22 '16 at 20:17
  • $\begingroup$ @HDE226868 Converted to wiki at Gerald's request so that others can make the necessary modifications to beef up the answer. Gerald is currently busy. $\endgroup$ – called2voyage Oct 26 '16 at 18:07

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