Cosmology, Page 102

Cosmology, Page 102: [Previous Page] [Next Page] [Class Home Page] Textbook pages 462 - 469

General Relativity and the Shape of the Universe

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Einstein's theory for general relativity tells us that the presence of mass curves space-time. Such an analogy was used in describing the environment around Black Holes. There we represented warping of space-time with an infinite 2-dimensional sheet. We will do the same to show how space-time can be warped based on the mass contained in our universe:

Closed Universe
A closed universe has what is called positive curvature, and looks like a sphere. In a closed universe, when you get to very, very large scales, the circumference of a circle is smaller than 2*pi*R and all the angles in a triangle add up to MORE than 180.

Flat Universe
In a flat universe, zero curvature, geometry works the way you learned in school. The angles of a triangle add up to 180, and the circumference of a circle equals 2*pi*R no matter how you curl or manipulate a sheet of paper.

Open Universe
An open universe has negatively curved space. It looks like a "saddle" or "potato chip". In such a universe, the circumference of a circle is GREATER than 2*pi*R and the angles in a right triangle add up to LESS than 180.

Open, closed or flat: the universe has no edge!

How do we measure which universe we live in? One way is by counting the number of galaxies as we go to larger and larger distances. Either it is consistent with a flat universe, or there are either too many or too few galaxies.

For a great website explaining more of this, go HERE. If we count too few galaxies at larger distances, which universe are we living in?

Spacetime Wrinkles

Closed Universe A closed universe has what is called positive curvature, and looks like a sphere. In a closed universe, when you get to very, very large scales, the circumference of a circle is smaller than 2piR and all the angles in a triangle add up to MORE than 180.
Flat Universe In a flat universe, zero curvature, geometry works the way you learned in school. The angles of a triangle add up to 180, and the circumference of a circle equals 2piR no matter how you curl or manipulate a sheet of paper.
Open Universe An open universe has negatively curved space. It looks like a "saddle" or "potato chip". In such a universe, the circumference of a circle is GREATER than 2piR and the angles in a right triangle add up to LESS than 180.