The Cosmological Principle and the Universe

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SUMMARY

The discussion centers on the cosmological principle, which asserts that the universe is homogeneous and isotropic on large scales. It is established that the principle allows for a spatially finite universe with a finite amount of matter, particularly in geometries such as the 3-sphere. The conversation also clarifies that a 3-torus does not conform to the cosmological principle unless it is a flat 3-torus. The complexities of defining ratios involving infinities are highlighted, indicating that such questions may be unanswerable.

PREREQUISITES
  • Understanding of the cosmological principle
  • Familiarity with spatial geometries: 3-sphere, flat geometry, 3-torus
  • Basic knowledge of curvature types: positive, zero, negative
  • Concepts of infinity in mathematics
NEXT STEPS
  • Research the implications of the cosmological principle on cosmology
  • Study the properties of different spatial geometries in cosmology
  • Explore the mathematical treatment of infinity and its applications in physics
  • Learn about the implications of curvature in the universe's structure
USEFUL FOR

Astronomers, cosmologists, physicists, and students interested in the foundational principles of the universe and its geometric properties.

greswd
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The cosmological principle seems to hold well, and would imply an infinite amount of matter in the universe if the universe is flat and unbounded
 
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Your question has an undefined numerator, an undefined denominator and is unmeasurable.
 
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greswd said:
The cosmological principle seems to hold well, and would imply an infinite amount of matter in the universe

No, it wouldn't, since the cosmological principle by itself allows a spatially finite universe containing a finite amount of matter, provided it has the spatial geometry of a 3-sphere.
 
Vanadium 50 said:
Your question has an undefined numerator, an undefined denominator and is unmeasurable.
wouldn't the ratio be the odds of the guess being correct?

And just asking on what one might think the odds are
 
PeterDonis said:
No, it wouldn't, since the cosmological principle by itself allows a spatially finite universe containing a finite amount of matter, provided it has the spatial geometry of a 3-sphere.
what about a 3-torus?
 
greswd said:
what about a 3-torus?

A 3-torus does not obey the cosmological principle (unless you mean a flat 3-torus, which falls into the "flat" category below). Only three spatial geometries do: 3-sphere (constant positive curvature), flat (zero curvature), 3-hyperboloid (constant negative curvature).
 
greswd said:
wouldn't the ratio be the odds of the guess being correct?

Only if the ratio is a ratio of finite numbers.

greswd said:
just asking on what one might think the odds are

And what @Vanadium 50 was telling you is that this question is unanswerable because the ratio of two infinities is not well-defined.

Thread closed.
 

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