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10 Pages

### lec2n

Course: ASTRO 480, Fall 2009
School: Penn State
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Word Count: 1758

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Universe Einstein's Newtonian gravity gave the energy of the universe as R R 2 8 - G0 3 R0 R 3 = 2E R2 (2.01) In the relativisitic case, the equation is very similar R R 2 8 - G0 3 R0 R 3 kc2 =- 2 + R 3 (2.02) Here, k is constant which defines the curvature of the universe. Note that k only appears when divided by R2 (which is not measureable). Thus, to simplify things, we can choose the units of R...

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Universe Einstein's Newtonian gravity gave the energy of the universe as R R 2 8 - G0 3 R0 R 3 = 2E R2 (2.01) In the relativisitic case, the equation is very similar R R 2 8 - G0 3 R0 R 3 kc2 =- 2 + R 3 (2.02) Here, k is constant which defines the curvature of the universe. Note that k only appears when divided by R2 (which is not measureable). Thus, to simplify things, we can choose the units of R such that k is either 0, 1, or -1. The value k = 1 represents a universe with positive curvature, like a sphere; k = -1 reflects negative curvature, like a saddle. In the critical case, where k = 0, the universe is flat. The other new variable is a Cosmological Constant. You can think of it as a pressure term which supplies a new repulsive (or attractive) force that is directly proportional to distance, R = R (2.03) If one wants the universe to be static, then one needs to include this additional term to counter-act the attractive force of gravity. (There are other reasons to add in a Cosmological Constant, but this was the origin...
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