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Understanding Radiation and Vacuum Expansion in Cosmological Models

This lecture explores the dynamics of radiation and vacuum expansion, highlighting key concepts such as scale factors, doubling times, and the interplay between gravitational forces and cosmic density. It discusses the mathematical relationships governing the scale factor (S) during various cosmic epochs, from the early universe to the GUT transition and inflationary phase. The underlying physics such as gravitational constant (G), matter density, and vacuum density are examined, along with the implications of exponential growth and cosmic inflation on the structure of the universe.

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Understanding Radiation and Vacuum Expansion in Cosmological Models

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  1. Lecture 31 updates

  2. Radiation and Vacuum Expansion Vacuum: S 2t 10-16 Scale Factor: S Radiation: S t 0.0 0.0 1.0 2.0 3.0 Time: t

  3. Time taken to double size Exponential Doubling Time Vacuum: S 2t 10-16 Scale Factor: S 0.0 0.0 1.0 2.0 3.0 Time: t

  4. Time to “fall” Newton’s gravitational constant Density of the system Vacuum density:  Matter density:  Density:  Collapse time Doubling time Orbit time “Falling” Time 1 (G  ) tfall ≈

  5. The Power Of Doubling Growth 1 8 231 16 32 48 64

  6. 100 Doublings 2100 ≈ 1030 rice grains fill the earth 100 doublings

  7. Scale Factor (S) 10-30 10-25 10-20 10-15 10-10 1080 1030 Density (tons/cm3) GUT transition 1020 1040 Temperature (K) Unknown physics Super-symmetry breaking Electroweak transition 1010 1 1 ps 10-40 10-30 10-20 1 10-10 Time (seconds)

  8. Scale Factor (S) 10-28 10-30 10-25 10-20 10-15 10-10 1080 1030 1073 tons/cm3 Density (tons/cm3) GUT transition 1020 1040 Temperature (K) Unknown physics Super-symmetry breaking Electroweak transition 1010 1 1 ps 10-40 10-30 10-20 1 10-10 Time (seconds)

  9. ?? GUT transition & inflation Inflation Reheating Scale Factor (S) 10-30 10-25 10-20 10-15 10-10 1080 1030 Density (tons/cm3) 1020 1040 Temperature (K) Unknown physics 1010 1 10-40 10-30 10-20 1 10-10 Time (seconds)

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