The Cosmological Principle and the Universe

In summary, the cosmological principle holds well and suggests an infinite amount of matter in a flat and unbounded universe. However, this principle allows for a spatially finite universe with a finite amount of matter if it has the spatial geometry of a 3-sphere. The odds of a guess being correct cannot be determined as it involves a ratio of two infinities, which is not well-defined.
  • #1
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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  • #2
Your question has an undefined numerator, an undefined denominator and is unmeasurable.
 
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  • #3
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.
 
  • #4
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
 
  • #5
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?
 
  • #6
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).
 
  • #7
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.
 

1. What is the Cosmological Principle?

The Cosmological Principle is a fundamental concept in cosmology that states that the universe is homogeneous (the same at every point) and isotropic (the same in all directions) on a large scale. This means that the laws of physics and the distribution of matter are consistent throughout the universe.

2. How does the Cosmological Principle relate to the Big Bang Theory?

The Big Bang Theory is based on the assumption that the universe is governed by the Cosmological Principle. This principle allows for the explanation of the large-scale structure and expansion of the universe as observed by astronomers.

3. What evidence supports the Cosmological Principle?

One of the main pieces of evidence for the Cosmological Principle is the cosmic microwave background radiation, which is a remnant of the early universe and is nearly uniform in all directions. Additionally, observations of the large-scale distribution of galaxies and the overall structure of the universe also support the idea of homogeneity and isotropy.

4. Are there any exceptions to the Cosmological Principle?

While the Cosmological Principle is generally accepted as a fundamental concept in cosmology, there are some exceptions that have been observed. For example, on a smaller scale, the universe is not completely homogeneous and isotropic, as there are variations in the distribution of matter and the laws of physics. Additionally, the presence of dark matter and dark energy challenges the idea of a completely uniform universe.

5. How does the Cosmological Principle impact our understanding of the universe?

The Cosmological Principle is crucial in our understanding of the universe and its origins. It allows us to make predictions and test theories about the evolution and structure of the universe. It also serves as a foundation for other important concepts in cosmology, such as the expansion of the universe and the formation of galaxies and other large-scale structures.

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