Huldrich

It is not the mathematical side I don't understand: assuming that space is evenly filled with galaxies, one can suppose that they are like particles in an infinite volume and approximately constitute a cosmological fluid. So you get a matter density, which you can integrate over the volume to obtain the amount of matter contained in it. Since the volume is infinite, the matter is too. That is perfectly clear to me. The problem is that I feel uneasy with a universe of infinite matter, not because there is no center. I just think that it is not physical and it should be possible to show some contradiction. I first thought that it should lead to Olber's paradox. But it doesn't because there the universe is static while here it is expanding. As can be read in Hartle's book Gravity, light rays can only reach us from a certain distance in a expanding infinite universe, so even if the sky contained an infinite number of stars their light that reaches us would be finite and the sky would not be bright but dark. My point of view is rather philosophical. I very like a spherical closed universe because it is similar to Earth's surface on which we live. Its volume is also expanding but finite as well as the matter in it. Such a universe is much more familiar to me than an infinite one with infinite matter. Physically spoken, matter cannot be infinite in my opinion even though mathematically it can. It's just a subjecive feeling. But I am sure that someone will once find an argument against infinite universes or experimental data will show it. As can be read on Wikipedia: The Shape of the Universe "The latest research shows that even the most powerful future experiments (like SKA, Planck..) will not be able to distinguish between flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10−4. If the true value of the cosmological curvature parameter is larger than 10−3 we will be able to distinguish between these three models even now." If the universe is infinite flat, the cosmological curvature parameter is exactly 1. It seems to me that it is very unlikely that a continuous physical parameter can exactly be a natural number. And with the dark matter that is more and more discovered, the cosmological curvature parameter, which in fact is made up of densities, is more likely to be > 1 than < 1. In this case the universe is spherical. I think this eventualty would have pleased most Greek and medieval philosophers...

I appreciate your effort Spyman, thanks. However, you don't tell me something new. I already wrote in my first question that I know that a flat infinite universe is supposed to be homogenous as for its distribution of mass. So evidently there can be no boundary. But in this case an infinite universe must contain an infinite amount of matter. This is what I don't understand. It may not contradict with Olber's paradox since it uses another model as stated by DH. I just can't figure out an infinite universe filled everywhere with matter. It's nonsense. In my opinion, expansion of space implies that the universe is closed, like a 3-sphere for instance. The amount of matter in such models is finite. Models that lead to infinite matter can be ruled out in my view although I can't exactly say why.

Ok, but if the quantity of matter is infinite, how then I have to understand the big bang, which is seen as singularity? Does it make sense that to say that an infinite quantity of matter was concentrated at one point at time 0 ? And when the universe expanded, in any case matter must have been distributed over a limited region of the infinite universe, otherwise it wouldnt be a singularity. I think that homogeneity of matter is only required to be over a limited region, maybe over the visible universe. Unfortunately I cant read this explicitly in Hartle's book. This is why I am not sure about it. Maybe someone can confirm?

Hi, I am new here and I don't know if I am in the right forum. I have a master in physics and am actually reading the book Gravity of James B. Hartle. I could not answer a question about infinite, homogenous and isotropic models of the universe based on the FRW-metric. This model requires that matter is distributed evenly all over the universe. But since it is a flat infinite model, homogeneity implies that the quantity of matter should be infinite, which cannot be because of Olber's paradox. However, if matter is finite the universe cannot be homogenous at all points. There must be some kind of cloud of matter, beyond which matter starts to rarefy to finally disappear completely. So homogeneity contradicts infinity in my opinion. I am also asking myself if there can be a observable difference between the expansion of space and expansion of matter in an infinite universe. In a closed system, it is clear that space expands. But an expanding flat infinite universe doesn't make sense to me: it can't get bigger because it's already infinite. So I am asking myself if it is equivalent to say that only matter expands, not space, in such a model. Do you agree or can you show me where I am wrong?