Infinity is not merely a very large number.
It means to be truly without limit.
The region of the Universe close enough for us to observe contains
over a hundred billion galaxies and trillions of dwarf galaxies.
A dwarf galaxy typically contains several billion stars.
A normal galaxy contains an average of several hundred billion stars.
Added together, this is far more stars than all the grains of sand on Earth.
This is just the section of the universe that is close enough to us for us to observe.
What if we travel beyond the region of the universe that is visible to us?
There are three possibilities.
One possibility is that we live in what we call an Open Universe.
Here, just as the number pie contains an infinite number of digits
without any repeating patterns, so too would the Universe
possess an infinite number of stars and galaxies.
Another possibility is that we live in what we call a Closed Universe.
Suppose we travel along a straight path that extends without a beginning or an end.
If we live in a closed Universe, then even if we travel along a straight
path without any turns, it can eventually return back to where it started.
This is possible because objects with mass cause a curvature in space-time.
This is what causes the apparent force of gravity binding the
moon to the Earth, Earth to the sun, and sun to the galaxy.
There only appears to be a force,
when in reality everything is just following straight lines.
If the density of the universe is high enough,
space-time can completely curve into itself to form a closed universe.
We would be analogous to two dimensional beings living on a sphere,
able to travel only on the surface, and never go inside.
This sphere is expanding, and the rate of expansion is accelerating.
According to Albert Einstein’s Theory of Relativity,
nothing can travel through space faster than the speed of light.
But, the expansion of space itself causes the distance between
faraway objects to increase faster than even light can travel.
The farther apart two galaxies are from one another,
the faster the distance between them increases.
The distance between galaxies that are extremely far apart
increases faster than even the speed of light.
This is true in both in an open Universe and in a closed Universe.
Therefore, even if we live in a closed Universe, it would still not be possible to
circumnavigate the entire Universe and return to where we started, as was shown.
The expansion of space is too rapid.
Thought, the expansion of space does not increase the
distance of the moon to the Earth, or the distance of the
Earth to the sun, or the distance of the sun to the other stars in our Galaxy.
These are bound together by the apparent force of gravity,
and the expansion of space does not overcome this.
The only distances that are increasing are the distances between Galaxies.
Every observer in the Universe will see all the Galaxies
moving away from them as if they are at the center of expansion.
This is true both in an open Universe, and in a closed one.
If the density of the Universe is high enough, we live in a
closed Universe, and its shape is analogous to a sphere.
A triangle drawn on the surface of this sphere will violate Euclidian Geometry,
in that its angles will add up to a value greater than 180 degrees.
If the density of the Universe is low enough, we live in
an open Universe and its shape is analogous to a saddle.
A triangle drawn on the surface of this saddle will violate Euclidian Geometry
in a different way, in that its angles will add up to a value less than 180 degrees.
There is a third possibility.
If the density is exactly in between that of a closed Universe and
that of an open Universe, then we live in what we call a flat Universe.
A flat universe would still have curvature near the stars and planets,
but it would be flat in the sense that a triangle drawn on a large section of the
Universe would obey Euclidian Geometry, and have its angles add to 180 degrees.
A flat Universe, like an open Universe,
contains an infinite number of stars and planets.
The Earth appears flat to us when we are able to see only a tiny portion of it.
As far as the accuracy of our measurements can tell,
we seem to live in a flat universe.
However, this may be simply because we are able
to observe only a tiny part of the entire Universe.
Both a sphere and a saddle look flat when you zoom in and look at only a tiny section.
Just as ancient people tried to discover if the earth was round or flat,
we now are trying to discover the shape of the entire Universe.