I The Cosmological Principle and the Universe

[greswd]

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

 

[Vanadium 50]

Your question has an undefined numerator, an undefined denominator and is unmeasurable.

 

[PeterDonis]

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.

 

[greswd]

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

 

[greswd]

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?

 

[PeterDonis]

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).

 

[PeterDonis]

wouldn't the ratio be the odds of the guess being correct?

Only if the ratio is a ratio of finite numbers.

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.