On size scales of billions of light years, the universe is assumed to be uniform. This makes the universe models simpler and ``more reasonable''---if we lived in an unusual part of the universe, then it would be almost impossible to understand the universe as a whole from observing our surroundings. The discovery of the long superclusters may seem to endanger this assumption. On large enough scales though, the universe has many superclusters in all directions. It is like a large bowl of tapioca pudding, one spoonful of pudding looks like any other spoonful, even though, there are the small tapioca pieces.

The idea of a uniform universe is called the **cosmological
principle**.
There are two aspects of the cosmological principle:

- The universe is
**homogeneous**. This means there is no preferred observing position in the universe. - The universe is also
**isotropic**. This means you see no difference in the structure of the universe as you look in different directions.

The cosmological principle is a Copernican idea. It means we are not in a
special place. Every observer at a given *cosmological time* will see the
same thing, such as the same Hubble law. ``Cosmological time'' in this context
means the time measured from some common event like the creation of the
universe. Everyone at the same cosmological time will measure the same age of
the universe. The cosmological principle allows the universe to change, or
evolve, throughout time.

An extension of the cosmological principle called the **perfect
cosmological principle** says that the universe also does
not change with time; there is no evolution. Therefore, in an expanding universe,
*new* matter
must be continually created. This violates a central rule of nature known
as the *law of the conservation of mass.* This law says that the total
amount of mass does not change---mass is not created from nothing or destroyed.
However, the amount of new matter that would need to be created for the
perfect cosmological principle to be true is quite small---only one
hydrogen atom per cubic centimeter every 10^{15} years. This is
approximately one hydrogen atom/Houston Astrodome every year---a very small amount!
As described in the
previous chapter, the
increase in the number of quasars at large distances from us, is strong evidence of
a universe that DOES change, or evolve. Other evidence for a changing universe is
given later in this chapter.

To help you understand what curved spacetime means, let's use the analogy of a
two-dimensional world curving into the third dimension. Pretend you are
confined to the surface of a balloon and you only know about ``front'', ``back'',
``left'', and
``right'', but not ``up'' and ``down''. In your 2D universe you cannot see the
third dimension. Your universe appears flat. Yet you know that your 2D universe must
be curved because if
you walk in a straight line, you eventually arrive back at where you started!
The balloon universe has a finite size but *no edge.*
You also know that the angles of large triangles add up to a number larger than
180°! For example, on the balloon the lines of longitude running
north-south intercept the equator at a 90° angle and converge at the poles.
So a triangle made of one point on the equator + the north pole + another
point on the equator will have the angles add up to *more* than 180°.
In a truly flat universe, the angles would add up to exactly
180°. You would be able to deduce that your universe is *positively*
curved.

On sufficiently small scales the surface looks flat so the regular geometry
rules apply. The angles in a small triangle add up to 180°. Here on the
surface of the Earth, the Earth looks flat to us because the curvature of the
Earth is so much larger than we are. The universe does not have to curve back on itself
as shown in the illustrations above. This type of *positively-curved* universe
is usually easier to picture, but the curvature could be the opposite. In a
*negatively-curved* universe, the universe curves away from itself. A
two-dimensional analogy would look like a saddle. The angles in large triangles would
add up to less than 180°. Like the positively-curved universe, there would be no
center on the surface and *no edge.*

Rather than setting up BIG triangles in the universe, astronomers can use how the number of galaxies increases with increasing distance. If the universe has zero curvature and the galaxies are spread roughly uniformily in the universe, then the number of galaxies should increase linearly with ever greater volume. Lines defining an angle spread out in straight lines. If the universe has positive curvature, then the number of galaxies increases with greater volume then decreases with very large volumes. Lines defining an angle spread out at first and then converge at great distances. If the universe has negative curvature, then the number of galaxies increases more rapidly with with ever greater volume than a flat universe. Lines defining an angle diverge at increasing angles as the lines curve away from each other.

The idea of a curved surface also explains why astronomers in every galaxy will see the other galaxies moving away from it and, therefore, derive the same Hubble Law. Go back to the balloon analogy, imagine that there are flat houses on it. As the balloon expands, the elastic material moves the houses apart from each other. A person sitting on their front porch see everybody else moving away from her and she appears to be the center of the expansion.

Now add another dimension and you have our situation. Just like there is not new
balloon material
being created in the 2D analogy, new three-dimensional space is not being
created in the expansion. Like any analogy, though, the balloon analogy has its limits.
In the analogy, the balloon expands into the region around it---there is space beyond
the balloon. However, with the expanding universe, space *itself* is expanding
in three dimensions---the whole coordinate system is expanding.
*Our universe is NOT expanding ``into'' anything ``beyond''.*

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last updated: April 29, 2013

Author of original content: Nick Strobel