I thought I had a handle on the whole big bang/cosmic expansion/background radiation thing. Then I was reading a university website that discussed the COBE findings, that map they made of the time of last scattering, etc. In it, the writer was assuring the many folks who wrote in to him that the universe, at its birth, was already infinite in size.
Huh? I thought the universe even NOW wasn’t infinite. Here was my understanding:
Bang. Everything in the entire cosmos is contained in a singularity.
Space rapidly expands and cools
300,000 years later, it cools enough to turn transparent
About 14 billion years later, here we are. Space is still expanding, the universe may be finite, but there’s no edge (like the flat surface of a balloon is finite but with no edge)
Now, I realize that “the big bang happened everywhere”–i.e., since the whole universe was touching back then, every part of space was filled with that bang and is still filled with that severly red-shifted radiation.
But how big was the universe at the time of the big bang? A minute later? Or 300,000 years later? Shouldn’t it have been only 300,000 light-years across at the most?
Your confusion is between (at least) two different usages of the word “universe.” This is sometimes used to refer to the observable universe, i.e. everything close enough to us that light can have traveled from it to us in less time than the age of the universe. On the other hand, “universe” is often used to refer to the whole universe, whether we can see it or not.
You see this confusion in the line you quote. The first time “universe” is used it refers to the observable universe; the second time it’s used, it refers to the whole thing. This is a common confusion; I think there needs to be a catchier term than “observable universe” (or visible universe, etc.) to differentiate the two, because as it is the word “observable” tends to get dropped somewhere along the way.
The size of the observable universe is finite, since the universe has a finite age. The size of the whole universe isn’t really subject to empirical observation, since everything other than the observable universe is by definition unobservable. There are various expanding-universe models (such as the Friedman-Robertson-Walker model) which can be used to guess what we think the rest of the universe looks like, and these can be tested on the part of the universe we can see, but there are both finite and infinite models which agree with the data known so far.
I think that Cosmic Inflation Theory has it that the Universe underwent a huge growth spurt at the very beginning of the Big Bang. If it didn’t then the observable Universe should be the same size as the Universe itself. If Inflation theory is true (and it has a lot of support) then the Universe grew quicker than the speed of light so that the Universe as a whole is bigger than our observable Universe.
Nonetheless I have always been of the understanding that the Universe is finite in size (finite but unbounded as in the baloon example). Given that light speed is a limit to how fast we can travel (barring some sci-fi like hyperspace travel or something) and that the universe is presumably growing at light speed today it is to all practical purposes infinite to us. You can travel as long and as fast as you want and you will never be able to circumnavigate the Universe but will travel forever away from your starting point.
The universe is not “growing at light speed” whatever that means. The entire universe is expanding more or less uniformly, so the recession velocity is proportional to the distance. At a certain distance, space is receeding at c. At greater distances, the recession velocity is greater than c. This is not in violation of Relativity, because it is space itself that is expanding. Nothing is moving faster than light in its vicinity.
Does the Inflation theory still possit that the big bang started in an infinitessimally small space and expanded? Or could the big bang have occured over a very large (maybe infinite) space ‘all at once’?
There was presumably a change from space not existing (‘pre big bang’ if that can mean anything) where all physics laws are unusable, to a space existing (‘post big bang’). Why do we postulate that the initial size of space was finite and very small? What is the reason not to consider it coming into being huge (or infinite)? WOuld this not be cleaner than the postulated faster than light expansion happening after the big bang?
DrMatrix does this expansion rate give an expected volume of the universe when you postulate starting from zero size, and expanding at the same rate for 14 billion years?
Also does this then lead to the distance between very distant points in the Universe increasing at faster than c, because the space between the points is expanding?
It depends. The basic FRW expanding-universe model is finite but unbounded for some values of its parameter, but it is infinite for other values. The inflating-balloon analogy is essentially the closed, positive-curvature FRW model, but if the curvature is 0 or negative then the universe becomes infinite.
The FRW model is just one class of possible models, though. If you add a cosmological constant (which seems to be needed to explain the latest data) or allow the universe as a whole to have nontrivial topology then other models are possible; you can have, for instance, a finite flat universe.
As I understand it, the inflation theory was developed to explain the problem of the homogeneity of the observable universe. If you look in any direction, the cosmic microwave background radiation is pretty much the same, even when the standard FRW models predict that those two regions of the universe (say, the cosmic North and South poles) shouldn’t have been able to see one another–so how did they know what temperature they should be at? Inflation says that at some point in the early universe a very small region, small enough that the points within the region could thermally equilibrate, was blown up very rapidly, so that the regions earlier able to reach thermal equilibrium became the entirety of the observable universe today.
Neither inflation nor the noninflationary theories (like FRW) require that the big bang start from a point. What they start from is a “singularity”, which is a region of spacetime at which some value in the equations becomes infinite. This is usually taken by cosmologists as an indication that some physics beyond GR is needed to describe the behavior here, so talking about the behavior of spacetime near a singularity is pretty speculative. For the FRW balloon model (a closed, finite universe with positive curvature), the volume of the universe approaches zero as you approach the singularity, and the curvature becomes infinite. But for the flat-universe FRW model, the volume of the universe is infinite for all t>0, which is more like the situation you ask about.
Ah. The most telling thing I’ve seen in a long time. So then, more explicitly, “singularity” = “we don’t know”.
Thanks for the finite/infinite clarification. I thought finite had been pretty well agreed upon; apparently there is still much discussion. And I thought the “flat universe” issue dealt more with the ultimate fate of the universe, not its current scale/geometry (i.e., endless expansion, or eventual gravitational collapse; not finite/infinite CURRENT size).
There are several related but different issues here. One is the issue of the overall curvature of spacetime; that is, of whether the universe at large scales is “flat” or not. The surface of a piece of paper is flat, meaning that circles of arbitrary diameter drawn on the paper have the same ratio of circumference to diameter (pi). The surface of an inflated balloon is not flat, though; a large circle will have a circumference-to-diameter ratio of less than pi because the balloon curves inward. This is called “positive” curvature. (It is also possible to describe surfaces of negative curvature, where the circumference of a large circle is more than pi times its diameter. These look something like a saddle.)
Another is the issue of whether the whole universe is finite or infinite in spatial size. A balloon-type universe, where the overall structure of space is that of the surface of a three-dimensional sphere, is finite, for example; but a flat space with the structure of Cartesian space (R[sup]3[/sup]) is infinite. A third issue is the question of whether the total lifetime of the universe is finite (“big crunch” models, where the universe recollapses, in a process something like the inverse of the big bang) or infinite.
The simplest cosmological models of the universe assume the presence only of “normal” matter and energy (like atoms and light), along with the usual assumptions that spacetime looks the same all over (“homogeneous” and “isotropic”). For these models, all three of these issues are coupled: a universe with positive curvature has finite size and finite lifetime, and a universe with zero or negative curvature has infinite size and infinite lifetime.
But the presence of non-normal types of energy, like the cosmological constant (which seems to be nonzero based on recent data), changes this. It is possible, for appropriate choice of the cosmological constant, to make a universe with positive curvature have infinite lifetime, or to make a universe with negative or zero curvature have finite lifetime. (Current data still indicates that we live in a nearly-flat universe with infinite lifetime, though; the sign of the cosmological constant in our universe seems to speed up the expansion, not slow it down.)
I think it’s also possible to have universes which are more complicated topologically. As in the old game Asteroids where your ship could run off one side of the screen and return on the other, the universe can (I think) be finite but unbounded due to some global periodicity, apart from the local density-curvature relations provided by the Einstein field equations. This sort of solution doesn’t have to obey the curvature-size constraint, so flat universes might not need to have infinite size. I don’t know much about these solutions though.
Discover magizine regularly has articles discussing this type of thing in accessible terms. http://www.discover.com/recent_issue/index.html
The cover article from the 4/02 issue discussies inflation. The cover of that issue had a red marble on it, which they presented as the universe - actual sized - whatever fraction of a second after BB.
The cover story from 4/03 - Was Einstein Wrong suggests an alternative to inflation.
Basically, yes. One caveat is that sometimes a “singularity” is just the fault of the coordinates being used (the usual example being the North Pole in polar coordinates, which doesn’t have a well-defined longitude). These are called “coordinate singularities” and aren’t real, physical singularities. In Schwarzschild’s spherically-symmetric solution to the Einstein equations there is a singularity at the Schwarzschild radius. This was thought to be physical for a while, but coordinate transformations were later discovered that showed that in fact it is only a coordinate singularity; no new physics was required to understand the behavior there, just a better choice of coordinate system. (The singularity at the center is still a singularity in these new coordinates, though. The spacetime curvature, a physical value which is invariant under coordinate transformations, becomes infinite there, so no coordinate transformation can clean that singularity up.)