I.E. WHAT IS THE OVERALL SHAPE OF THE UNIVERSE? WILL IT EXPAND FOREVER, WILL IT EVENTUALLY CONTRACT, OR ... ?

For a very nice detailed tutorial:

see http://www.astro.ucla.edu/~wright/cosmolog.htm

Beethoven's magificent op106

Which is it? 

Measurements (before the two listed below as Bulletins 1 and 2) have determined the approximate value of Omega_{0 = ~0.3.  Some accept this value as likely accurate and therefore accept that the Universe must expand forever, without boundary.}

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_{Omega0 refers to a density ratio that defines the overall structure of the Universe and is equal to the total mass and energy present per unit volume of space at any given time divided by the amount of mass at that moment required to exactly "balance" the Universe....}

_{Omega0 can be considered to have two additive components - one from the total mass present within the universe, and one from a term that Einstein defined as a "cosmological constant." The term defines energy inherently present as space is created. If the cosmological constant term is anything greater than zero, as space continues to be created (through the Universe's expansion) energy is created to fill that space. For the purposes of this discussion, these two factors are summed = Omega0 and the cosmological constant is assumed to = zero (the only evidence to the contrary are observational studies of high redshift supernova -- very open to interpretational error).}

_{_________________________________________________________________________}

_{If Omega0 is less than one:}

• _{The density of the Universe is insufficient to stop its current expansion, and the Universe will go on expanding forever, containing its total matter in an ever enlarging space with matter and energy density becoming smaller and smaller.}
•  

• _{If  Omega0 is greater than one:}
• _{The Universe must stop expanding and then contract, ending in a "Big Crunch."}
• _{If  Omega0 is exactly equal to one:}
• The Universe will forever expand to a bounded limit, never reaching that limit and never contracting.

-- BUT --

Astronomers and cosmologists have calculated that if the Universe at one nanosecond after the Big Bang had a density of 4.5 x 10^23 grams per cubic centimeter of space, then the structure of our Universe would forever be "flat" (critical density), resulting in its expansion, ever more slowly, to a bounded limit, but never quite reaching that limit. (This is equivalent to walking half way to a door, then walking half the distance remaining, and so on; you would never quite get there, and the door would forever remain just out of reach -- the limit of your travels.)

If the Universe at one nanosecond after the Big Bang had a density which was only one part in 4.5 x 10^23 than the 4.5 x 10^23 grams/cc of space, then we would already be in the Big Crunch phase (which we are not). That is equivalent to a balance of 1 gram in 447 sextillion grams!

On the other hand, if the Universe at one nanosecond after the Big Bang was only one gram less than the critical density, we would observe a different Universe than the one in which we live.

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In summary: We know that the Universe's density at one nanosecond after the Big Bang had to be  within less than one gram/cc of 4.5 x 10^23 grams/cc in order that our observed Universe could exist.  In other words, the Universe finds itself perched, within 1 part in 447 sextillion, between three different structural realities and destinies:

Open - expanding without limit, vs.

Bounded - forever expanding to a bounded limit, vs.

Closed - expanding to a limit then contracting to a "Big Crunch."

How likely is it that the density of the Universe was within 1 part in 447 sextillion at one nanosecond of time, but was - just ever so slightly off - , resulting in either a boundless expansion or a Big Crunch?  

If you are not sufficiently amazed by the number 1 part in 447 sextillion, consider that this very delicate balance is even finer:  When one analyzes the critical density at a much earlier moment following the Big Bang, long before it reached the age of one nanosecond -- one that is at the limits of our knowledge -- the balance at critical density equals one part in 10^⁵⁹!

So then, the question is:   Did the Universe at its birth begin in a very nearly perfect balance  (within an order of  one part in10⁵⁹) but  was, nonetheless, not exactly at that balance point?

_{In my opinion, accepting that the answer is "yes" is inconsistent with the esthetics of this beautiful Universe.  Arguing on the grounds that accepting such a tiny tip of the balance away from what is an extreme degree of precision is unaesthetic and, I believe, unlikely.}

_{It seems much more likely that with further refinements in our detection of dark matter, etc., we will find that Omega0 is not 0.3, or nearly equal to 1.0, but is instead exactly equal to 1.0; it is therefore exceedingly likely that we live in a flat universe, one that will expand forever but never quite reach its given boundary.}

_{The next exciting question is:  How did the Universe spring to existence in such a perfect balance of expansion rate and density to exactly bound it at a limit?  One thought is that matter and energy can be thought of as positive and that gravity can be thought of as negative energy; if the two are locked in equality and symmetry, then that balance might explain the Omega0 balance.}

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_{NOTE: For a discussion regarding the question of whether or not a cosmological constant of greater than zero exists, check out: "The Runaway Universe" by Donald Goldsmith (Perseus Books, Cambridge, Mass.; copyright 2000, ISBN 0-7382-0068-9).}

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_{BULLETIN 1: 4/2000 - New findings from balloon based telescope: "Boomerang" --- FLAT UNIVERSE!}

_{www.physics.ucsb.edu/~boomerang/}

_{www.nsf.gov/od/lpa/news/press/00/pr0025.htm}

_{http://arXiv.org/format/astro-ph/0005123}

_{http://arXiv.org/format/astro-ph/0005124}

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_{Other opinions, information, and discussions are welcome: email gde@ringnebula.com}

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