Part of universe mapped by coordinates

In summary: It's not the full picture, you know.In summary, the conversation discusses the radial coordinate, r, in a positively curved universe. The value of r ranges from 0 to 1, which may suggest that it is a local map. However, without more context or detail, it is difficult to determine. The conversation also mentions the normalization of r and the construction of the Robertson-Walker metric for positive curvature. The conversation ends with a discussion about the choice of coordinates and the diffeomorphism of the universe to a 3-sphere.
  • #1
bloby
112
8
I read in a positively curved universe the radial r coordinate ranges from 0 to 1. Is it just a local map?
 
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  • #2
bloby said:
I read in a positively curved universe the radial r coordinate ranges from 0 to 1. Is it just a local map?
Why do you suggest that it's a local map? Because the value of r ranges only from 0 to 1? Sounds to me like r is ranging over the full radius of the manifold, and is simply normalized so that r_max = 1. However, without context or more detail, I can't be of any more help.
 
  • #3
bapowell said:
However, without context or more detail, I can't be of any more help.

In Kolb&Turner and in my cours the coordinates of a point on a 3-sphere are the projection on an hyperplane (the equatorial plane if on a 2-sphere). They construct the Robertson-Walker metric for positive curvature this way. But then only one half of the sphere is mapped, isn't it? The huge value the line element takes when r tends to one or R(you are right it's normalized r) is simply the consequence of the choice of coordinates? (Forgive me for my bad english)((If you live on the North, to name a point, of a 2-sphere you can map each points by an angle and a length (->r*pi) or even a comoving length (r/R*pi) but these are not the usual coordinates, aren't they?))

I suggest that it's a local map because I read a constant positive curvature means the universe is "only" diffeomorphic to a 3-sphere.
 

1. What does it mean to map a part of the universe by coordinates?

Mapping a part of the universe by coordinates means that scientists have assigned specific numerical values to different locations in space. These coordinates can be used to pinpoint the location of objects in the universe and create a visual representation of their positions.

2. How is this mapping done?

This mapping is done using specialized instruments such as telescopes, satellites, and radars. These instruments collect data on the positions of objects in the universe and use mathematical calculations to determine their coordinates.

3. Why is mapping the universe by coordinates important?

Mapping the universe by coordinates allows scientists to better understand the structure and organization of the universe. It also helps in identifying and tracking the movement of celestial objects, studying the evolution of the universe, and making predictions about future events.

4. Is the mapping of the universe by coordinates accurate?

The accuracy of mapping the universe by coordinates depends on the precision of the instruments used and the complexity of the objects being mapped. With advancements in technology, the accuracy of these mappings has significantly improved over time.

5. Can anyone access these coordinates and maps?

Yes, many organizations and institutions make these coordinates and maps publicly available for educational and research purposes. However, some data may be restricted for privacy or security reasons.

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