1. How does the universe expand? What is expansion? Newtonian derivation of FRW-equations Problems with FRW: causality General Relativity derivation of FRW- equations

2. What is expansion?

3. Newtonian Derivation

4. FRW-equations

5. Special Relativity: 2 postulates: The laws of physics are the same for all observers The speed of light is equal to the same constant for all observers

6. Causality Space-time according to O1: The guy who’s watching TV Space-time according to O2: The guy who is running from O1 to the TV

7. The OPERA-experiment

8. GR-derivation of FRW-equations Events given by 4-vectors A tensor, like, is a generalised matrix Metric tensor defines distances Indices are raised/lowered by and it’s matrix inverse: Energy momentum tensor is Einstein’s equation (16 equations!) is:

9. Homogeneity & Isotropy demand: Flat space, k = 0 and sum = 180° Spherical space, k = +1, sum > 180° Hyperbolical space, k = -1, sum < 180°

10. The calculation Put this into Einstein’s equation (16!): Mathematica gives: only 2 independent equations: k = 0 Flat space k = +1 Spherical space k = -1Hyperbolical space

11. Conclusion: How Does the universe expand? Homogeneity & Isotropy: Gravity: Equation of state: Special relativity demands v < c if causality should hold Does not apply for distant galaxies, since communication is impossible