Density parameter and curvature index

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Discussion Overview

The discussion centers around the relationship between the density parameter (Ω) and the curvature index (κ) in cosmology. Participants explore whether κ is dependent on Ω or if it can exist independently, particularly in the context of different values of Ω.

Discussion Character

  • Debate/contested, Technical explanation

Main Points Raised

  • One participant questions if κ follows directly from Ω or if it can have an independent existence, particularly asking if κ must equal 1 when Ω>1.
  • Another participant asserts that if Ω>1, κ must not be 0 and must share the same sign as Ω-1, suggesting a defined relationship between the two parameters.
  • Several participants request definitions of κ, indicating a need for clarity on the term.
  • It is noted that the definition of κ may vary, with one participant mentioning that the (-1,0,1) classification could simplify the discussion.

Areas of Agreement / Disagreement

The discussion remains unresolved, with multiple competing views on the relationship between Ω and κ, as well as differing definitions of κ itself.

Contextual Notes

Participants express uncertainty regarding the definitions and implications of κ, indicating that the discussion may depend on specific definitions and interpretations that are not fully agreed upon.

Ranku
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For Ω=1, κ=0. Does the value of κ simply follow from the value of Ω, or can its value have an independent existence? So if Ω>1, does κ have to be 1?
 
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Context would be useful. I don't want to guess what you mean.
 
Ranku said:
So if Ω>1, does κ have to be 1?
Yes, by definition. Since Ω=1 is the critical density - the density at which the universe is flat - any other value of Ω necessitates that the k parameter is not 0 and has the same sign as Ω-1.
 
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Likes   Reactions: Jaime Rudas and Ranku
Define k for me.
 
The definition of k seems to have more than one option. For example the (-1,0,1) option simplifies your question.
 

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