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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.

User Contributions:

1
Keith Phemister
⚠
Sep 13, 2024 @ 11:23 pm
Copied from above: If the Universe were infinitely old, infinite in extent, and filled
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun.
Why would anyone assume this? Certainly, we have directions where we look that are dark because something that does not emit light (is not a star) is between us and the light. A close example is in our own solar system. When we look at the Sun (a star) during a solar eclipse the Moon blocks the light. When we look at the inner planets of our solar system (Mercury and Venus) as they pass between us and the Sun, do we not get the same effect, i.e. in the direction of the planet we see no light from the Sun? Those planets simply look like dark spots on the Sun.
Olbers' paradox seems to assume that only stars exist in the universe, but what about the planets? Aren't there more planets than stars, thus more obstructions to light than sources of light?
What may be more interesting is why can we see certain stars seemingly continuously. Are there no planets or other obstructions between them and us? Or is the twinkle in stars just caused by the movement of obstructions across the path of light between the stars and us? I was always told the twinkle defines a star while the steady light reflected by our planets defines a planet. Is that because the planets of our solar system don't have the obstructions between Earth and them to cause a twinkle effect?
9-14-2024 KP

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