Can there be an infinity of stars in the Universe?

I have a mind puzzle.

Can there be an infinity of stars in the Universe ?

I have 2 opposed reasonings, yet I don’t find any flaw in them. Can you help me here ?

Answer A : No, the number of stars cannot be infinite.

In the whole Universe, at an instant t, there are W molecules of water. This number may be very big, but it has a definite value. The same goes for stars. Each of all the stars at the instant t has her own size, and we can give her a name. We can list all of them, and we can sort them from nearest to farthest — if we are omniscient, of course.

Answer B : Yes, the number of stars can be infinite.

Space has no finite volume. Space has no ending wall. If I advance into space, I can always go further. Wherever I go, space is by default filled with… vacuum. But it could be otherwise. [I am not sure of this point.] Space could be by default filled with… air. So there would be +∞ molecules of air in the Universe. We can apply this reasoning to stars. Let’s say there is, in average, 1 star / 1060 m3. So, in the total infinite volume of space, there would be +∞ stars. When I advance into space, I would keep meeting new stars, without end. Like in these video games in which mountains keep appearing as far as you walk.

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Your 'Answer A' assumes that $W$ is a finite value and then concludes that it's a finite value. It's a clear case of begging the question. –  Stan Liou Aug 2 '14 at 23:54

Theoretically yes, there can be infinitely many stars. Since this space you're talking about is better described by general relativity and Einstein's field equations. One of its solutions describes the universe as being spatially infinite.

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+1, though under the assumptions of large-scale homogeneity and isotropy (which are motivated mainly by cosmic background radiation), there are four qualitatively different kinds of possible spatial geometries, two of which are infinite (Euclidean $3$-space and hyperbolic $3$-space). –  Stan Liou Aug 2 '14 at 23:57

The simple answer is "no." This is easily demonstrated by looking at the sky at night. It is dark, and therefore the number of stars is finite. If there were an infinite number of stars, light would be streaming in to the Earth from all point in the sky, which would make the sky very (lethally) bright.

Further evidence stems from the cosmic microwave background radiation, which is highly uniform in all directions (isotropic and homogeneous), and about 3 degrees above absolute zero, which is completely inconsistent with an infinite number of stars in the universe.

Third is the finite volume and energy of the universe, where "universe" here refers to all that can be observed from Earth. This volume is defined by the speed of light combined with the time since the Big Bang. It is clearly finite based on strong observational evidence and theoretical work, which in turns precludes an infinite volume or energy in the universe.

Finally, current cosmology strongly favors a multiverse with a multitude of "pocket universes", of which ours is one. This view is based on the idea of eternal inflation as developed by Alan Guth and others. It should not be confused with the at present speculative notion of a cosmic landscape as found in string theory.

Instead, the notion of a vast and possibly infinite number of pocket universes is a consequence of current theory, which in turn is based on good observational evidence. That said, each of these pocket universes is separated from all others, so light from one cannot reach another. As above, this scenarios also precludes an infinite number of stars.

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The dark sky at night is not a problem for me. The numerous stars are very far away, and are very far from each other. So there is a lot of black between lights. This is my explanation. This dark sky at night is a paradox for some people, and many explanations are proposed. –  Nicolas Barbulesco Aug 2 '14 at 17:30
-1 the first two paragraphs are complete nonsense. The third effectively substitutes "observable universe" for "universe", a qualifier that is not present in the question. –  Stan Liou Aug 2 '14 at 23:52
This is a known fallacy. –  Envite Aug 4 '14 at 11:24

It depends on if the universe as a whole is perceived finite or infinite.

• If the universe is infinite, the possible amount of stars is too.
• If the universe in finite, the possible amount of stars is too.