# Closed Universe

by on August 6, 2009

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Dark, cold stars from the young Universe could still be here today (University of Utah)

The closed universe model is one of the offshoots of the Big Bang theory. As more proofs supported one theory as to how our universe began (i.e., the Big Bang), scientist’s studying cosmology began to shift their attention to a question on the other end of the line – how will our universe end?

Scientists are suggesting 4 possible ways as to how our universe may end: a Big Freeze, a Big Rip, a Big Crunch, or a Big Bounce. Of course, there are other theories but these 4 are the most widely discussed. To predict the Universe’s ultimate fate, scientists need to determine a few important factors. The most significant of which are its density and its shape.

Of all the proposed shapes, 3 models stand out: open, closed, and flat.

In terms of the Friedmann equations, a closed universe is obtained when the density parameter, represented by the capital Greek letter Omega (Ω), is greater than unity or Ω > 1. For comparison Ω = 1 denotes a flat universe, while Ω < 1 denotes an open one. Ω is defined as the ratio of the observed density to the critical density. The currently accepted value for the critical density is about 10-30 grams per cubic centimeter.

The Friedmann equations were introduced by Alexander Friedmann in order to relate all factors that contribute to the expansion of space based on a homogeneous and isotropic model of the Universe and derived out of Einstein’s General Relativity.

Notice how both the density and shape of the Universe are supposed to be closely related. For example, a closed universe should be expected for an actual density greater than the critical density. This would subsequently mean that its future will most likely end in either a Big Crunch or Big Bounce.

A closed universe can be imagined to have a positive curvature, much like a sphere. Hence, if somehow you can travel in one direction for a very long time, you can eventually end up in the same position as where you started. Furthermore, if you have two parallel lines on the surface, they will eventually intersect if you trace their paths over large distances, just like the longitude lines in a globe.

The most accurate measurements made in relation to the Big Bang are being gathered through the WMAP (Wilkinson Microwave Anisotropy Probe). The information is based on accurate measurements of the cosmic microwave background (CMB) fluctuations. Interestingly, WMAP measurements are indicative of a flat universe despite the fact that its own density measurements show values lower than the critical density.

This is where the idea of dark energy, which is believed to provide the driving force for the Universe’s increasing rate of expansion, comes from.

We’ve got a few articles that touch on closed universe here in Universe Today. Here are two of them:

NASA also has some more:

Tired eyes? Let your ears help you learn for a change. Here are some episodes from Astronomy Cast that just might suit your taste:

Sources: Hyperphysics, NASA

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