Expert: Philip Stahl - 9/28/2009

Question
QUESTION: Where is cosmology now on the overall shape of the universe? Is it a big sphere, with the galaxies all moving away from each other? Then what is in the center, a big space? What about the old question, if one headed out from earth in a spaceship on a straight line trajectory, with the earth always in the center of the rear view mirror, where would you go? Would you wind up eventually heading back to earth? Is the universe analogous in three dimensions to the two dimensional surface of a sphere, finite yet unbounded?


ANSWER: Hello,

Rather than trying to deal with this textually, I think you will find most of your answeres addressed in this short video on the shape of the universe. If you still have questions after watching it, let me know.

http://science.discovery.com/videos/cosmos-shape-of-the-universe.html



---------- FOLLOW-UP ----------

QUESTION: Thanks, but Carl Sagan's short exposition seems a bit dated and simplistic.  How about a link that explains some of the latest findings of the WMAP related to this question.  I've read a lot of the basic websites, including the WMAP website, but I still don't understand if the universe is very close to 'flat' then is there an edge to it, a boundary?  And what about the unseen part of the universe, moving away faster than light because of the increased expansion rate?  Is the universe like a closed mobius loop, everything inside it and nothing outside of it?

Answer
Hello again,

Okay, well I wasn't quite sure what your background was, so preferred to err on the side of caution and being conservative.

Before one can go into the geometry of the cosmos, one first needs to choose a template. In terms of Einstein's theory of general relativity, the one most chosen is the one for the so-called F-R-W cosmologies or Friedmann-Robertson-Walker. The Einstein field equations typically used for assessment of shape parameters is:

(dR/dt /R)^2 = (8 pi)/ 3 (G_N rho) – k / R^2

The first term denotes the square of the rate of the space scale R, in relation to R. Meanwhile, k denotes the curvature.

Using a particular F-R-W template, one can have:

k = +1 (positive curvature - spherical geometry)

k = -1 (negative curvature - hyperbolic or horse saddle type geometry)

k = 0 (flat or Euclidean universe)

Universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can have curvature k = +1); 'critical' (k=0)or 'open' (can be k = -1), respectively

Now, to determine whether any F-R-W cosmological template leads to deceleration or not, we need to find the cosmic density parameter:

Omega = rho / rho_c

where the denominator refers to the critical density. Thus if:

rho (greater than) rho_c

(c = critical)

then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large rho is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.

Current data, e.g. from Boomerang and other satellite detectors shows that  rho_c ~ 0.3 or that:

rho = 0.3 (rho_c)

This means the universe is "flat" but it doesn't mean there is any "boundary". Please review Sagan's video again where he goes into this.  (Btw, when we say "flat" we don't mean literally flat Euclidean, but flat space-time)


Thus, the current mass density is barely three-tenths of the critical value to assure a re-collapse. (I.e. that  rho <  rho_c so there is no danger of the cosmos decelerating.)

Re: unseen part of the universe moving at faster than the speed of light, you are referring to the intervening *space* between the expanding components (e.g. galaxy clusters).  Technically, then there are no "parts" of which to speak or write "moving faster than light", since the description applies to what is happening topologically to the intervening *space*.  (Why the cosmos is actually ~ 93 billion LY across)

Using terms like "inside" or "outside" is counter-productive and not particularly enlightening since the universe is self-contained. As hard as it is to accept (and I don't have the time here to go into all the details on this, or how the intervening space in expansion is displacing at faster than light rates, or why space-time need not have any boundary) the cosmos can expand without expanding into anything else. The difficulties in conception arrive from too closely embracing the typical balloon analogies and not appreciating the nuances.

I believe what you need here, is not merely five or even twenty pages of trying to explain all the details you require, but actually taking a course which explains this all and does it nicely.

The course I am referencing can be found here:

http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1830


It is a great deal right now, and it is excellent. (My brother ordered it and found it very enlightening)

If you don't wish to invest any money then check out this open course link for MIT:

http://ocw.mit.edu/OcwWeb/Physics/8-224Exploring-Black-Holes--General-Relativity

containing video lecture links

What I am saying here is that the nature of the questions you're asking and level of difficulty go far beyond what even a lengthy 'All experts' answer allows. As I said earlier, I have neither the time, energy or ...I will confess, motivation...to fully deal with what you're asking at the level it requires.