# Fraction of the Universe that is unobservable

I was watching this talk by Leonard Susskind. Near the end of his talk, he mentions how, because of the accelerating expansion of the Universe, there is a horizon to the Universe beyond which we cannot observe anything. Then, he makes the following claim, which I have never heard before, quoting:

The universe is at least 1000 times larger in volume than the region what (sic) we can ever see. The rest is beyond our horizon.

(You can see this at the top of the slide at 53:30 in the video.)

What I would like to know is this:

1. Is this number of "at least 1000 times" widely accepted?
2. How do we/can we know that?
• If the universe is infinite (as widely believed by cosmologists), and we can observe only a finite portion of it, then the universe is infinitely larger than we can see (not just 1000 times). In most contexts though, physicists tend to disbelieve infinite values, so 1000 times seems sufficiently large to convey the same general idea. Sep 16 '18 at 23:00
• @D. Halsey: That cosmologists widely accept that the universe is infinite is news to me. Isn't it one of the deductions from GR that the universe is finite in extent - however large? Sep 17 '18 at 0:47
• Um... I was under the impression that the open or closed nature of the universe is still undecided, with the observed density still within observational uncertainty of the critical density. As to the original question, there should probably be an "in this theory" in there someplace.
– user93146
Sep 17 '18 at 1:33
• @puppetsock The visible fraction of the does not really depend on the curvature parameter $k$. I also agree with Moribur Ullah that it is not generally assumed that the universe is infinite. However, I am also a bit surprised by Lenny's statement. Any chance he may have confused it with the number of causally disconnected patches that make up our CMB?
– user178876
Sep 17 '18 at 2:31

If the universe is has a positive spatial curvature on the largest scale then there is a very natural shape---the 3-sphere---which it can adopt, and this shape has a finite volume. If the universe is flat or negatively curved, on the other hand, then the universe could perhaps be infinite, but it could also have various topologies which allow it to be finite.

It is doubtful whether we puny humans could ever have warrant to claim to know that the universe is infinite. How could we possibly know that? We can not. All the data we ever acquire is consistent with a finite universe. (Any unqualified claims that it is infinite that may be made in popular presentations of cosmology are certainly overblown).

Measurements of the spatial curvature, chiefly from the CMB radiation combined with models of early universe physics (the BAO process), give a value slightly above zero but consistent with zero: $$\Omega - 1 = 0.006 \pm 0.020$$ (This is a parameter that relates to curvature; the universe is flat if $$\Omega = 1$$). This suggests that the universe is either spatially flat or it is a 3-sphere with a very large radius of curvature. In the latter case, the most natural interpretation is to say that it is indeed such a 3-sphere and then its overall radius would be considerably larger than the radius of the observable universe, and this is perhaps the origin of the comment by Susskind.

• "All the data we ever acquire is consistent with a finite universe." +1 The idea of "infinite" comes from modern confused mathematics starting with the illogical definition of "infinity" as an "extended number". Physicists nave more common sense and generally agree that nothing real is infinite, because infinite cannot be observed, but more precisely because infinite is meaningless. Thus "the universe is infinite" is a meaningless statement both physically and mathematically. Jul 1 '19 at 21:33

This video from PBS Space Time explains it fairly well.