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Understanding the Expansion of the Universe: A Comprehensive Study

This article explores the complex nature of the universe's expansion, starting with defining expansion itself and delving into Newtonian and General Relativity derivations of the Friedmann-Robertson-Walker (FRW) equations. It discusses the implications of causality, the influence of homogeneity and isotropy, and the significance of different spatial curvatures. Additionally, it highlights the role of the speed of light in maintaining consistency across observations. By analyzing these aspects, we aim to provide an insightful overview of how the universe expands and its fundamental principles.

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Understanding the Expansion of the Universe: A Comprehensive Study

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Presentation Transcript

  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 O2: The guy who is running from O1 to the TV Space-time according to O1: The guy who’s watching 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!): • Mathematicagives: only 2 independent equations: k = 0 Flat space k = +1 Spherical space k = -1 Hyperbolical 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

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