Gothic_J

I was told something freaky recently - the universe is finite, but is shaped like an egg, so you wont notice. the surface of the egg is zillions of galaxies, and inside is empty space, where the galaxies used to be.

Lobstrosity

If inflation is correct, you're wrong. It's looking more and more like inflation is correct.

Lobstrosity

Unless I'm mistake as to the prevailing view of modern cosmology, everything wasn't once in finite conditions. The metric for our universe, if flat, would be given by the familiar:

dl� = a�(dr� + r�d&#952� + r�sin�&#952 d&#966�)

This arises from the Friedmann model, which assumes a priori that the universe is homogeneous and isotropic--assumptions that do have some empirical backing. Now note that this metric describes a universe of infinite volume (so long as a is not zero) since r ranges from zero to infinity. Theta ranges from zero to pi and phi ranges from zero to two pi. a is a scale factor that determines the overall scale of the spatial metric. This scale factor is not a function of r, &#952, or &#966, which means that it does not violate homogeneity or isotropy. It can be, however, a function of time. The Hubble constant is defined as [(da/dt) / a].

Basically, what you have is a universe that is always infinite in size but whose characteristic length scale is changing with time.

Or maybe I'm talking out of my ass. Let's wait for someone with more working knowledge of cosmology to come along and set us straight (as this is a question I've always wondered about--people always describe the origins of the universe as a single finite point, so then how does something finite expand into something infinite?). All I know is that the current cosmological models are founded on the principle of homogeneity and a finite universe certainly isn't homogeneous. I also know that the model that is currently used for cosmology (the Friedmann model) deals with a universe of infinite extent (so long as it's flat or open), though perhaps this model is not completely accurate.

Tetlepanquetzatzin

I see Lobstrosity has already made some good points. Here are my points, which to some extent is a repetition of Lobstrosity's post.
Correct. The Big Bang model is based on Weyl's postulate, stating that if we follow the geodesics of all particles backwards in time they will eventually converge to the same point.
The Big Bang is a singularity in the sense that general relativity no longer remains a valid approximation very close to the Big Bang.

The universe has either been finite during all its history or infinite during all its history. This is consistent with Weyl's postulate, because the cosmological metric (given in co-moving coordinates) is of the form

ds^2 = (c dt)^2 - a(t)^2 dr^2

Here, dt is a small difference in time coordinates and dr is a small difference in spatial coordinates (this is somewhat simplified). Even if no coordinates change, the distance will change in time because of the scale factor a(t) (this is how the expansion of the universe is represented in the math). The scale factor goes to zero when get close to the Big Bang, so no matter how large difference in spatial coordinates is the spatial contribution to the distance will go to zero close to the Big Bang (compare with Weyl's postulate!). The scale factor will make all particle trajectories converge as we approach the Big Bang even if the universe is infinite.
Space-time does not come from anything (except, possibly, a black hole in another space-time a la Smolin), since "come from" is a concept that only makes sense within a space-time. The Big Bang is not an explosion.
It is easy to become a little confused by this subject. That is good, because confusion is often the state that preceedes insight. Once you study the metrics used in our cosmological models you will realize that there is no finite-to-infinite transition, and your confusion will be converted into insight. When we say that the universe was small in the past we mean nothing more nor less than that the scale factor was small.

beachmaster

Perhaps the only way to view the quandary is that the universe is finite with infinite potential (open universe)?

eh

It's not just infinite because it will exist without end, but because it is spatially infinite. It has always been infinite, even at the instant of the big bang. In such a case the empty space between galaxies expands over time, but the overall size remains infinite. In the early universe, everything becomes very dense. Only a finite universe is very small at this time, though exactly how small is an open question.

Jesse

If the universe is closed, then 3-D space would be curved and finite in a way similar to the surface of a 4-D hypersphere (just like the surface of a 3-D sphere is a curved and finite 2-D surface). But if the universe is flat or open, space is infinite. Whether our universe is closed, flat, or open depends on the density of mass/energy in space (see this page for more)--I believe cosmological observations suggest it is flat or very close to it, but it might be possible that it's close to flat but not exactly so, in which case perhaps it could be closed with a very large but finite size.

If the universe is closed, then as you go back in time it's like the 4-D hypersphere shrinks, so the total volume of space decreases. If the universe is flat or open, then space was infinite at every finite time after the big bang. But space still can "expand" in a flat, infinite universe--think of a giant chess board where all the squares are expanding in size simultaneously (like what you'd see if you zoomed in on a picture of a chess board), but the pieces stay the same size and remain at the center of their respective squares. Likewise, as you go back in time the squares shrink while the pieces stay the same size and get crowded closer together. At the moment of the big bang, the area of each square would go to zero, as would the distance between any pair of squares.

Friar Bellows

Unless, of course, the topology of the universe is multiply connected. Then it could be finite despite having a constant spatial curvature of zero (i.e. spatially flat) everywhere.

Solanalos

Thank you all for your insights. They have helped me tremendously. The scale factor aspect rearranged my concept. I do see it a lot more clearly than before, but not enough to allow me to fully visualize it. I'm having a hard time imagining a scale factor of zero in an infinite universe. I am, however, sneaking peeks when I ponder for a while. Goddamned freaky universe!

spacer1

Do you mean that there are only ever or larger or smaller scales of measurement? If so, it seems to suggest an infinite universe, since it assumes no limits. Or, might you be saying that infinity and zero are only idealized limits which can never be achieved in reality?
Might it be better to say that the area of each square and the distance between squares approaches zero? Infinitely small doesn't equal zero, surely. It must be an infinitely small quantity of the thing we are measuring, which must, therefore, have existence. Wouldn't zero size (in all dimensions) denote non-existence?