Defining Large-Scale Isotropy: A Formal Definition

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This discussion focuses on developing a formal definition of 'large-scale isotropy' in cosmology, a concept that lacks precise articulation in existing literature. The author emphasizes that while isotropy definitions are clear, the 'large-scale' aspect remains ambiguous and poorly defined. The conversation suggests that this ambiguity complicates the understanding of isotropy in cosmological contexts. The author encourages readers to refer to a linked thread for more comprehensive insights before returning to this post.

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  • Understanding of cosmological principles and terminology
  • Familiarity with the concept of isotropy in physics
  • Knowledge of hypersurfaces and foliations in mathematics
  • Basic grasp of metric spaces and shortest path calculations
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  • Research the mathematical foundations of hypersurfaces in cosmology
  • Explore the implications of isotropy in the context of the Cosmic Microwave Background (CMB)
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Cosmologists, astrophysicists, and researchers interested in the mathematical foundations of cosmological theories and the precise definitions of isotropy in large-scale structures.

andrewkirk
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This Insight is part of my attempt to develop a formal definition of ‘large-scale isotropy’, a concept that is fundamental to most cosmology, but that is nowhere that I have seen properly defined.
The definitions of isotropy are as precise as one could wish, but the ‘large-scale’ bit is in every case I have seen just a hand-wave. It turns out that it’s quite messy to try to make that ‘large-scale’ notion precise.
I made a thread on it, which is here.
It is possible that everything below is in that thread, in more up-to-date and better versions. But I am not sure, and as I don’t have time to check before the blogs are deleted, I’m posting the material below just in case.
If you’re interested in this topic, I’d suggest going to the linked thread first, and then only coming back to this post if there are links in the thread to it.
First, define ##\Sigma_t## as the hypersurface of constant time t in the foliation.
##d(t,P,Q)## is the length of the shortest path in ##\Sigma_t## from...

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