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[sci.astro] Cosmology (Astronomy Frequently Asked Questions) (9/9)
Section - I.04. What do people mean by an "open," "flat," or "closed" Universe?

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These different descriptions concern the future of the Universe,
particularly whether it will continue to expand forever.  The future
of the Universe hinges upon its density---the denser the Universe is,
the more powerful gravity is.  If the Universe is sufficiently dense,
at some point in the (distant) future, the Universe will cease to
expand and begin to contract.  This is termed a "closed" Universe.  In
this case the Universe is also finite in size, though unbounded.  (Its
geometry is, in fact, similar to the *surface* of a sphere.  One can
walk an infinite distance on a sphere's surface, yet the surface of a
sphere clearly has a finite area.)

If the Universe is not sufficiently dense, then the expansion will
continue forever.  This is termed an "open" Universe.  One often hears
that such a Universe is also infinite in spatial extent.  This is
possibly true; recent research suggests that it may be possible for
the Universe to have a finite volume, yet expand forever.

One can also imagine a Universe in which gravity and the expansion are
exactly equal.  The Universe stops expanding only after an infinite
amount of time.  This Universe is also (possibly) infinite in spatial
extent and is termed a "flat" Universe, because the sum of the
interior angles of a triangle sum to 180 degrees---just like in the
plane or "flat" geometry one learns in (US) high school.  For an open
Universe, the geometry is negatively curved so that the sum of the
interior angles of a triangle is less than 180 degrees; in a closed
Universe, the geometry is positively curved and the sum of the
interior angles of a triangle is more than 180 degrees.

The critical density that separates an open Universe from a closed
Universe is 1.0E-29 g/cm^3.  (This is an average density; there are
clearly places in the Universe more dense than this, e.g., you, the
reader with a density of about 1 g/cm^3, but this density is to be
interpreted as the density if all matter were spread uniformly
throughout the Universe.)  Current observational data are able to
account for about 10--30% of this value, suggesting that the Universe
is open.  However, motivated by inflationary theory, many theorists
predict that the actual density in the Universe is essentially equal
to the critical density and that observers have not yet found all of
the matter in the Universe.

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